ZF 3HP transmission

3HP 12 · 3HP 22
3HP 12 · 3HP 22
Overview
Manufacturer	ZF Friedrichshafen
Production	1963–1975 · 1973–1990
Model years	1963–1975 · 1973–1990
Body and chassis
Class	3-Speed automatic transmission for longitudinal and transverse engines
Chronology
Successor	ZF 4HP transmission family

The 3HP is a 3-speed Automatic transmission family with a hydrodynamic Torque converter with hydraulic control for passenger cars from ZF Friedrichshafen AG. In selector level position "P", the output is locked mechanically.

Key data

Gear ratios^[a]
Model	Version	First Deliv- ery	Gear				Total Span			Avg. Step	Components		Nomenclature
Model	Version	First Deliv- ery	R	1	2	3	Nomi- nal	Effec- tive	Cen- ter	Avg. Step	Total	per Gear^[b]	Gears Count	Cou- pling	Gear- sets	Input Shaft Diameter

Ravigneaux types													3^[b]	H^[c]	P^[d]
3HP 12	Small Engines	1963	−2.000	2.560	1.520	1.000	2.560	2.000	1.600	1.600	2 Gearsets 3 Brakes 2 Clutches	2.333				12 mm
3HP 12	Large Engines	1963	−2.000	2.286	1.429	1.000	2.286	2.000	1.512	1.512	2 Gearsets 3 Brakes 2 Clutches	2.333				12 mm
Simpson types
3HP 22	Large Engines	1973	−2.086	2.479	1.479	1.000	2.479	2.086	1.575	1.575	2 Gearsets 3 Brakes 2 Clutches	2.333				22 mm
3HP 22	Small Engines	1973	−2.086	2.733	1.562	1.000	2.733	2.086	1.653	1.653
3HP 22	Porsche 944	1981	−2.429	2.714	1.500	1.000	2.714	2.429	1.648	1.648

↑ Differences in gear ratios have a measurable, direct impact on vehicle dynamics, performance, waste emissions as well as fuel mileage 1 2 Forward gears only ↑ Hydraulic torque converter · German: Hydraulischer Wandler oder Drehmomentwandler ↑ Planetary gearing · German: Planetenradsätze

1963: 3HP 12
— Ravigneaux planetary gearset types —

History

The Ravigneaux planetary gearset types were first introduced in 1963 and produced through the mid-seventies and has been used in a wide range of cars. There are versions for longitudinal and transverse engines.

Planetary gearset concept

Planetary gearset concept: gear ratio quality^[a]
In-Depth Analysis^[b] With Assessment And Torque Ratio^[c] And Efficiency Calculation^[d]		Planetary Gearset: Teeth^[e]		Count	Nomi- nal^[f] Effec- tive^[g]	Cen- ter^[h]
		Ravigneaux		Count	Nomi- nal^[f] Effec- tive^[g]	Avg.^[i]

Model Type	Version First Delivery	S₁^[j] R₁^[k]	S₂^[l] R₂^[m]	Brakes Clutches	Ratio Span	Gear Step^[n]
Gear		R		1	2	3
Gear Ratio^[b]		${i_{R}}$ ^[b]		${i_{1}}$ ^[b]	${i_{2}}$ ^[b]	${i_{3}}$ ^[b]
Step^[n]		$-{\frac {i_{R}}{i_{1}}}$ ^[o]		${\frac {i_{1}}{i_{1}}}$	${\frac {i_{1}}{i_{2}}}$ ^[p]	${\frac {i_{2}}{i_{3}}}$
Δ Step^[q]^[r]					${\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}$
Shaft Speed		${\frac {i_{1}}{i_{R}}}$		${\frac {i_{1}}{i_{1}}}$	${\frac {i_{1}}{i_{2}}}$	${\frac {i_{1}}{i_{3}}}$
Δ Shaft Speed^[s]		$0-{\tfrac {i_{1}}{i_{R}}}$		${\tfrac {i_{1}}{i_{1}}}-0$	${\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}$	${\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}$
Torque Ratio^[c]		$\mu _{R}$ ^[c]		$\mu _{1}$ ^[c]	$\mu _{2}$ ^[c]	$\mu _{3}$ ^[c]
Efficiency $\eta _{n}$ ^[d]		${\frac {\mu _{R}}{i_{R}}}$ ^[d]		${\frac {\mu _{1}}{i_{1}}}$ ^[d]	${\frac {\mu _{2}}{i_{2}}}$ ^[d]	${\frac {\mu _{3}}{i_{3}}}$ ^[d]

3HP 12	160 N⋅m (118 lb⋅ft) Small engines 1963	25 32	32 64	3 2	2.5600 2.0000^[g]^[o]	1.6000
3HP 12	160 N⋅m (118 lb⋅ft) Small engines 1963	25 32	32 64	3 2	2.5600 2.0000^[g]^[o]	1.6000^[n]
Gear		R		1	2	3
Gear Ratio^[b]		−2.0000^[o]^[g] $-{\tfrac {2}{1}}$		2.5600 ${\tfrac {64}{25}}$	1.5200^[p] ${\tfrac {38}{25}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.7825^[o]		1.0000	1.6842^[p]	1.5200
Δ Step^[q]					1.1080
Speed		-1.2800		1.0000	1.6842	2.5600
Δ Speed		1.2800		1.0000	0.6842	0.8758
Torque Ratio^[c]		–1.9600 –1.9400		2.4836 2.4457	1.4928 1.4792	1.0000
Efficiency $\eta _{n}$ ^[d]		0.9800 0.9700		0.9702 0.9553	0.9821 0.9731	1.0000

3HP 12	Large Engines 1963	28 32	32 64	3 2	2.2857 2.0000^[g]^[o]	1.5119
3HP 12	Large Engines 1963	28 32	32 64	3 2	2.2857 2.0000^[g]^[o]	1.5119^[n]
Gear		R		1	2	3
Gear Ratio^[b]		−2.0000^[o]^[g] $-{\tfrac {2}{1}}$		2.2857 ${\tfrac {16}{7}}$	1.4286 ${\tfrac {10}{7}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.8750^[o]		1.0000	1.6000	1.4286
Δ Step^[q]					1.1280
Speed		-1.1429		1.0000	1.6000	2.2857
Δ Speed		1.1429		1.0000	0.6000	0.6842
Torque Ratio^[c]		–1.9600 –1.9400		2.2175 2.1836	1.4038 1.3914	1.0000
Efficiency $\eta _{n}$ ^[d]		0.9800 0.9700		0.9702 0.9553	0.9826 0.9740	1.0000

Actuated shift elements
Brake A^[t]					❶
Brake B^[u]					❶
Brake C^[v]		❶		❶
Clutch D^[w]				❶	❶	❶
Clutch E^[x]		❶				❶
Geometric ratios: speed conversion
Gear Ratio^[b] Ordinary^[y] Elementary Noted^[z]	$i_{R}=-{\frac {R_{2}}{S_{2}}}$	$i_{1}={\frac {R_{2}}{S_{1}}}$		$i_{2}={\frac {R_{2}(S_{1}+R_{1})}{S_{1}(S_{2}+R_{2})}}$		$i_{3}={\frac {1}{1}}$
Gear Ratio^[b] Ordinary^[y] Elementary Noted^[z]	$i_{R}=-{\tfrac {R_{2}}{S_{2}}}$	$i_{1}={\tfrac {R_{2}}{S_{1}}}$		$i_{2}={\tfrac {1+{\tfrac {S_{2}}{S_{1}}}}{1+{\tfrac {S_{2}}{R_{2}}}}}$		$i_{3}={\frac {1}{1}}$
Kinetic ratios: torque conversion
Torque Ratio^[c]	$\mu _{R}=-{\tfrac {R_{2}}{S_{2}}}\eta _{0}$	$\mu _{1}={\tfrac {R_{2}}{S_{1}}}{\eta _{0}}^{\tfrac {3}{2}}$		$\mu _{2}={\tfrac {1+{\tfrac {S_{2}}{S_{1}}}\eta _{0}}{1+{\tfrac {S_{2}}{R_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}}$		$\mu _{3}={\tfrac {1}{1}}$

↑ Revised 14 January 2026 Nomenclature $S_{n}=$ sun gear: number of teeth $R_{n}=$ ring gear: number of teeth $\color {gray}{C_{n}=}$ carrier or planetary gear carrier (not needed) $s_{n}=$ sun gear: shaft speed $r_{n}=$ ring gear: shaft speed $c_{n}=$ carrier or planetary gear carrier: shaft speed With $n=$ gear is $i_{n}=$ gear ratio or transmission ratio $\omega _{1;n}=\omega _{t}=$ shaft speed shaft 1: input (turbine) shaft $\omega _{2;n}=$ shaft speed shaft 2: output shaft $T_{1;n}=T_{t}=$ torque shaft 1: input (turbine) shaft $T_{2;n}=$ torque shaft 2: output shaft $\mu _{n}=$ torque ratio or torque conversion ratio $\eta _{n}=$ efficiency $i_{0}=$ stationary gear ratio $\eta _{0}=$ (assumed) stationary gear efficiency 1 2 3 4 5 6 7 8 9 Gear ratio (transmission ratio) $i_{n}$ — speed conversion — The gear ratio $i_{n}$ is the ratio of input shaft speed $\omega _{1;n}$ to output shaft speed $\omega _{2;n}$ and therefore corresponds to the reciprocal of the shaft speeds $i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}$ 1 2 3 4 5 6 7 8 9 Torque ratio (torque conversion ratio) $\mu _{n}$ — Torque Conversion — The torque ratio $\mu _{n}$ is the ratio of output torque $T_{2;n}$ to input torque $T_{1;n}$ minus efficiency losses and therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too $\mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}$ whereby $\eta _{n;\eta _{0}}$ may vary from gear to gear according to the formulas listed in this table and $0\leq \eta _{n;\eta _{0}}\leq 1$ 1 2 3 4 5 6 7 8 Efficiency The efficiency $\eta _{n}$ is calculated from the torque ratio in relation to the gear ratio (transmission ratio) $\eta _{n}={\frac {\mu _{n}}{i_{n}}}$ Power loss for single meshing gears is in the range of 1 % to 1.5 % helical gear pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range Corridor for torque ratio and efficiency in planetary gearsets, the stationary gear ratio $i_{0}$ is formed via the planetary gears and thus by two meshes for reasons of simplification, the efficiency for both meshes together is commonly specified there the efficiencies $\eta _{0}$ specified here are based on assumed efficiencies for the stationary ratio $i_{0}$ of $\eta _{0}=0.9800$ (upper value) and $\eta _{0}=0.9700$ (lower value) for both interventions together The corresponding efficiency for single-meshing gear pairs is ${\eta _{0}}^{\tfrac {1}{2}}$ at $0.9800^{\tfrac {1}{2}}=0.98995$ (upper value) and $0.9700^{\tfrac {1}{2}}=0.98489$ (lower value) ↑ Layout Input and output are on opposite sides Planetary gearset 2 (the outer Ravigneaux gearset) is on the input (turbine) side Input (turbine) shafts is, if actuated S₁ or S₂ Output shaft is R₂ (ring gear of the outer Ravigneaux gearset) ↑ Total ratio span (total gear ratio/total transmission ratio) nominal ${\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}$ A wider span enables the downspeeding when driving outside the city limits increase the climbing ability when driving over mountain passes or off-road or when towing a trailer 1 2 3 4 5 Total ratio span (total gear ratio/total transmission ratio) effective ${\frac {\omega _{2;n}}{max(\omega _{2;1};\|\omega _{2;R}\|)}}={\frac {min(i_{1};\|i_{R}\|)}{i_{n}}}$ The span is only effective to the extent that the reverse gear ratio matches that of 1st gear see also Standard R:1 Digression Reverse gear is usually longer than 1st gear the effective span* is therefore of central importance for describing the suitability of a transmission* because in these cases, the nominal spread conveys a misleading picture which is only unproblematic for vehicles with high specific power Market participants Manufacturers naturally have no interest in specifying the effective span Users have not yet formulated the practical benefits that the effective span has for them The effective span has not yet played a role in research and teaching Contrary to its significance the effective span* has therefore not yet been able to establish itself* either in theory or in practice. End of digression ↑ Ratio span's center $(i_{1}i_{n})^{\frac {1}{2}}$ The center indicates the speed level of the transmission Together with the final drive ratio it gives the shaft speed level of the vehicle ↑ Average gear step $\left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}$ There are $n-1$ gear steps between $n$ gears with decreasing step width the gears connect better to each other shifting comfort increases ↑ Sun 1: sun gear of gearset 1: inner Ravigneaux gearset ↑ Ring 1: ring gear of gearset 1: inner Ravigneaux gearset ↑ Sun 2: sun gear of gearset 2: outer Ravigneaux gearset ↑ Ring 2: ring gear of gearset 2: outer Ravigneaux gearset 1 2 3 4 Standard 50:50 — 50 % is above and 50 % is below the average gear step — With steadily decreasing gear steps (yellow highlighted line Step) and a particularly large step from 1st to 2nd gear the lower half of the gear steps (between the small gears; rounded down, here the first 1) is always larger and the upper half of the gear steps (between the large gears; rounded up, here the last 1) is always smaller than the average gear step (cell highlighted yellow two rows above on the far right) lower half: smaller gear steps are a waste of possible ratios (red bold) upper half: larger gear steps are unsatisfactory (red bold) 1 2 3 4 5 6 7 Standard R:1 — reverse and 1st gear have the same ratio — The ideal reverse gear has the same transmission ratio as 1st gear no impairment when maneuvering especially when towing a trailer a torque converter can only partially compensate for this deficiency Plus 11.11 % minus 10 % compared to 1st gear is good Plus 25 % minus 20 % is acceptable (red) Above this is unsatisfactory (bold) see also Total ratio span (total gear ratio/total transmission ratio) effective 1 2 3 Standard 1:2 — gear step 1st to 2nd gear as small as possible — With continuously decreasing gear steps (yellow marked line Step) the largest gear step is the one from 1st to 2nd gear, which for a good speed connection and a smooth gear shift must be as small as possible A gear ratio of up to 1.6667 : 1 (5 : 3) is good Up to 1.7500 : 1 (7 : 4) is acceptable (red) Above is unsatisfactory (bold) 1 2 3 From large to small gears (from right to left) ↑ Standard STEP — from large to small gears: steady and progressive increase in gear steps — Gear steps should increase: Δ Step (first green highlighted line Δ Step) is always greater than 1 As progressive as possible: Δ Step is always greater than the previous step Not progressively increasing is acceptable (red) Not increasing is unsatisfactory (bold) ↑ Standard SPEED — from small to large gears: steady increase in shaft speed difference — Shaft speed differences should increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one 1 difference smaller than the previous one is acceptable (red) 2 consecutive ones are a waste of possible ratios (bold) ↑ Blocks R₁ (ring gear of the inner Ravigneaux gearset) and S₂ (sun gear of the outer Ravigneaux gearset) ↑ Supports link with freewheel · blocks R₁ (ring gear of the inner Ravigneaux gearset) and S₂ (sun gear of the outer Ravigneaux gearset) in one direction ↑ Blocks C₁ and C₂ (the common carrier of the compound Ravigneaux gearset) ↑ Couples S₁ (sun gear of the inner Ravigneaux gearset) with the input (turbine) ↑ Couples S₂ (sun gear of the outer Ravigneaux gearset) with the input (turbine) ↑ Ordinary noted For direct determination of the ratio ↑ Elementary noted Alternative representation for determining the transmission ratio Contains only operands With simple fractions of both central gears of a planetary gearset Or with the value 1 As a basis For reliable And traceable Determination of specific torque and efficiency

1973: 3HP 22
— Simpson planetary gearset types —

History

The all new Simpson planetary gearset was introduced in 1973 and was produced through 1990 and has been used in a wide range of cars from Alfa Romeo, BMW,^[1] Citroën, Peugeot, and Fiat.^[2] There are versions for longitudinal and transverse engines.

Specifications

Specifications
Weight	45 kg (99 lb) with converter
Control	mechanical · hydraulic

Planetary gearset concept

Planetary gearset concept: gear ratio quality^[a]
In-Depth Analysis^[b] With Assessment And Torque Ratio^[c] And Efficiency Calculation^[d]		Planetary Gearset: Teeth^[e]		Count	Nomi- nal^[f] Effec- tive^[g]	Cen- ter^[h]
		Simpson		Count	Nomi- nal^[f] Effec- tive^[g]	Avg.^[i]

Model Type	Version First Delivery	S₁^[j] R₁^[k]	S₂^[l] R₂^[m]	Brakes Clutches	Ratio Span	Gear Step^[n]
Gear		R		1	2	3
Gear Ratio^[b]		${i_{R}}$ ^[b]		${i_{1}}$ ^[b]	${i_{2}}$ ^[b]	${i_{3}}$ ^[b]
Step^[n]		$-{\frac {i_{R}}{i_{1}}}$ ^[o]		${\frac {i_{1}}{i_{1}}}$	${\frac {i_{1}}{i_{2}}}$ ^[p]	${\frac {i_{2}}{i_{3}}}$
Δ Step^[q]^[r]					${\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}$
Shaft Speed		${\frac {i_{1}}{i_{R}}}$		${\frac {i_{1}}{i_{1}}}$	${\frac {i_{1}}{i_{2}}}$	${\frac {i_{1}}{i_{3}}}$
Δ Shaft Speed^[s]		$0-{\tfrac {i_{1}}{i_{R}}}$		${\tfrac {i_{1}}{i_{1}}}-0$	${\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}$	${\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}$
Torque Ratio^[c]		$\mu _{R}$ ^[c]		$\mu _{1}$ ^[c]	$\mu _{2}$ ^[c]	$\mu _{3}$ ^[c]
Efficiency $\eta _{n}$ ^[d]		${\frac {\mu _{R}}{i_{R}}}$ ^[d]		${\frac {\mu _{1}}{i_{1}}}$ ^[d]	${\frac {\mu _{2}}{i_{2}}}$ ^[d]	${\frac {\mu _{3}}{i_{3}}}$ ^[d]

3HP 22	320 N⋅m (236 lb⋅ft) 1973	35 73	35 73	3 2	2.4795 2.0857^[g]^[o]	1.5746
3HP 22	320 N⋅m (236 lb⋅ft) 1973	35 73	35 73	3 2	2.4795 2.0857^[g]^[o]	1.5746^[n]
Gear		R		1	2	3
Gear Ratio^[b]		−2.0857^[o]^[g] $-{\tfrac {2}{1}}$		2.4795 ${\tfrac {181}{73}}$	1.4795^[p] ${\tfrac {108}{73}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.8412^[o]		1.0000	1.6759^[p]	1.4795
Δ Step^[q]					1.1328
Speed		-1.1888		1.0000	1.6759	2.4795
Δ Speed		1.1888		1.0000	0.6759	0.8035
Torque Ratio^[c]		–2.0440 –2.0231		2.4303 2.4060	1.4699 1.4651	1.0000
Efficiency $\eta _{n}$ ^[d]		0.9800 0.9700		0.9802 0.9704	0.9935 0.9903	1.0000

3HP 22	Small Engines 1973	35 73	41 73	3 2	2.7331 2.0857^[g]^[o]	1.6532
3HP 22	Small Engines 1973	35 73	41 73	3 2	2.7331 2.0857^[g]^[o]	1.6532^[n]
Gear		R		1	2	3
Gear Ratio^[b]		−2.0857^[o]^[g] $-{\tfrac {73}{35}}$		2.7331 ${\tfrac {6,983}{2,555}}$	1.5616^[p] ${\tfrac {114}{73}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.7631^[o]		1.0000	1.7501^[p]	1.5616
Δ Step^[q]					1.1207
Speed		-1.3103		1.0000	1.7501	2.7331
Δ Speed		1.3103		1.0000	0.7501	0.9829
Torque Ratio^[c]		–2.0440 –2.0231		2.6755 2.6470	1.5504 1.5448	1.0000
Efficiency $\eta _{n}$ ^[d]		0.9800 0.9700		0.9789 0.9685	0.9928 0.9892	1.0000

3HP 22	Porsche 944 1981	28 68	32 64	3 2	2.7143 2.4286^[g]^[o]	1.6475
3HP 22	Porsche 944 1981	28 68	32 64	3 2	2.7143 2.4286^[g]^[o]	1.6475^[n]
Gear		R		1	2	3
Gear Ratio^[b]		−2.4286^[o]^[g] $-{\tfrac {17}{7}}$		2.7143 ${\tfrac {19}{7}}$	1.5000^[p] ${\tfrac {3}{2}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.8947^[o]		1.0000	1.8095^[p]	1.5000
Δ Step^[q]					1.2063
Speed		-1.1176		1.0000	1.8095	2.7143
Δ Speed		1.1176		1.0000	0.8095	0.9048
Torque Ratio^[c]		–2.3800 –2.3557		2.6562 2.6275	1.4900 1.4850	1.0000
Efficiency $\eta _{n}$ ^[d]		0.9800 0.9700		0.9786 0.9680	0.9933 0.9900	1.0000

Actuated shift elements
Brake A^[t]					❶
Brake B^[u]					❶	❶
Brake C^[v]		❶		❶
Clutch D^[w]				❶	❶	❶
Clutch E^[x]		❶				❶
Geometric ratios: speed conversion
Gear Ratio^[b] R & 2 Ordinary^[y] Elementary Noted^[z]	$i_{R}=-{\frac {R_{1}}{S_{1}}}$		$i_{2}={\frac {S_{2}+R_{2}}{R_{2}}}$
Gear Ratio^[b] R & 2 Ordinary^[y] Elementary Noted^[z]	$i_{R}=-{\tfrac {R_{1}}{S_{1}}}$		$i_{2}=1+{\tfrac {S_{2}}{R_{2}}}$

Gear Ratio^[b] 1 & 3 Ordinary^[y] Elementary Noted^[z]	$i_{1}={\frac {S_{1}(S_{2}+R_{2})+R_{1}S_{2}}{S_{1}R_{2}}}$				$i_{3}={\frac {1}{1}}$
Gear Ratio^[b] 1 & 3 Ordinary^[y] Elementary Noted^[z]	$i_{1}=1+{\tfrac {S_{2}}{R_{2}}}\left(1+{\tfrac {R_{1}}{S_{1}}}\right)$				$i_{3}={\frac {1}{1}}$
Kinetic ratios: torque conversion
Torque Ratio^[c] R & 2	$\mu _{R}=-{\tfrac {R_{1}}{S_{1}}}\eta _{0}$		$\mu _{2}=1+{\tfrac {S_{2}}{R_{2}}}\eta _{0}$
Torque Ratio^[c] 1 & 3	$\mu _{1}=1+{\tfrac {S_{2}}{R_{2}}}\eta _{0}\left(1+{\tfrac {R_{1}}{S_{1}}}\eta _{0}\right)$				$\mu _{3}={\tfrac {1}{1}}$

↑ Revised 14 January 2026 Nomenclature $S_{n}=$ sun gear: number of teeth $R_{n}=$ ring gear: number of teeth $\color {gray}{C_{n}=}$ carrier or planetary gear carrier (not needed) $s_{n}=$ sun gear: shaft speed $r_{n}=$ ring gear: shaft speed $c_{n}=$ carrier or planetary gear carrier: shaft speed With $n=$ gear is $i_{n}=$ gear ratio or transmission ratio $\omega _{1;n}=\omega _{t}=$ shaft speed shaft 1: input (turbine) shaft $\omega _{2;n}=$ shaft speed shaft 2: output shaft $T_{1;n}=T_{t}=$ torque shaft 1: input (turbine) shaft $T_{2;n}=$ torque shaft 2: output shaft $\mu _{n}=$ torque ratio or torque conversion ratio $\eta _{n}=$ efficiency $i_{0}=$ stationary gear ratio $\eta _{0}=$ (assumed) stationary gear efficiency 1 2 3 4 5 6 7 8 9 10 11 Gear ratio (transmission ratio) $i_{n}$ — speed conversion — The gear ratio $i_{n}$ is the ratio of input shaft speed $\omega _{1;n}$ to output shaft speed $\omega _{2;n}$ and therefore corresponds to the reciprocal of the shaft speeds $i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}$ 1 2 3 4 5 6 7 8 9 10 11 Torque ratio (torque conversion ratio) $\mu _{n}$ — torque conversion — The torque ratio $\mu _{n}$ is the ratio of output torque $T_{2;n}$ to input torque $T_{1;n}$ minus efficiency losses and therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too $\mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}$ whereby $\eta _{n;\eta _{0}}$ may vary from gear to gear according to the formulas listed in this table and $0\leq \eta _{n;\eta _{0}}\leq 1$ 1 2 3 4 5 6 7 8 9 Efficiency The efficiency $\eta _{n}$ is calculated from the torque ratio in relation to the gear ratio (transmission ratio) $\eta _{n}={\frac {\mu _{n}}{i_{n}}}$ Power loss for single meshing gears is in the range of 1 % to 1.5 % helical gear pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range Corridor for torque ratio and efficiency in planetary gearsets, the stationary gear ratio $i_{0}$ is formed via the planetary gears and thus by two meshes for reasons of simplification, the efficiency for both meshes together is commonly specified there the efficiencies $\eta _{0}$ specified here are based on assumed efficiencies for the stationary ratio $i_{0}$ of $\eta _{0}=0.9800$ (upper value) and $\eta _{0}=0.9700$ (lower value) for both interventions together The corresponding efficiency for single-meshing gear pairs is ${\eta _{0}}^{\tfrac {1}{2}}$ at $0.9800^{\tfrac {1}{2}}=0.98995$ (upper value) and $0.9700^{\tfrac {1}{2}}=0.98489$ (lower value) ↑ Layout Input and output are on opposite sides Planetary gearset 1 is on the input (turbine) side Input (turbine) shaft is, if actuated, S₁ or R₂ Output shaft is R₁ ↑ Total ratio span (total gear ratio/total transmission ratio) nominal ${\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}$ A wider span enables the downspeeding when driving outside the city limits increase the climbing ability when driving over mountain passes or off-road or when towing a trailer 1 2 3 4 5 6 7 Total ratio span (total gear ratio/total transmission ratio) effective ${\frac {\omega _{2;n}}{max(\omega _{2;1};\|\omega _{2;R}\|)}}={\frac {min(i_{1};\|i_{R}\|)}{i_{n}}}$ The span is only effective to the extent that the reverse gear ratio matches that of 1st gear see also Standard R:1 Digression Reverse gear is usually longer than 1st gear the effective span* is therefore of central importance for describing the suitability of a transmission* because in these cases, the nominal spread conveys a misleading picture which is only unproblematic for vehicles with high specific power Market participants Manufacturers naturally have no interest in specifying the effective span Users have not yet formulated the practical benefits that the effective span has for them The effective span has not yet played a role in research and teaching Contrary to its significance the effective span* has therefore not yet been able to establish itself* either in theory or in practice. End of digression ↑ Ratio span's center $(i_{1}i_{n})^{\frac {1}{2}}$ The center indicates the speed level of the transmission Together with the final drive ratio it gives the shaft speed level of the vehicle ↑ Average gear step $\left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}$ There are $n-1$ gear steps between $n$ gears with decreasing step width the gears connect better to each other shifting comfort increases ↑ Sun 1: sun gear of gearset 1: inner Ravigneaux gearset ↑ Ring 1: ring gear of gearset 1: inner Ravigneaux gearset ↑ Sun 2: sun gear of gearset 2: outer Ravigneaux gearset ↑ Ring 2: ring gear of gearset 2: outer Ravigneaux gearset 1 2 3 4 5 Standard 50:50 — 50 % is above and 50 % is below the average gear step — With steadily decreasing gear steps (yellow highlighted line Step) and a particularly large step from 1st to 2nd gear the lower half of the gear steps (between the small gears; rounded down, here the first 1) is always larger and the upper half of the gear steps (between the large gears; rounded up, here the last 1) is always smaller than the average gear step (cell highlighted yellow two rows above on the far right) lower half: smaller gear steps are a waste of possible ratios (red bold) upper half: larger gear steps are unsatisfactory (red bold) 1 2 3 4 5 6 7 8 9 10 Standard R:1 — reverse and 1st gear have the same ratio — The ideal reverse gear has the same transmission ratio as 1st gear no impairment when maneuvering especially when towing a trailer a torque converter can only partially compensate for this deficiency Plus 11.11 % minus 10 % compared to 1st gear is good Plus 25 % minus 20 % is acceptable (red) Above this is unsatisfactory (bold) see also Total ratio span (total gear ratio/total transmission ratio) effective 1 2 3 4 5 6 7 Standard 1:2 — gear step 1st to 2nd gear as small as possible — With continuously decreasing gear steps (yellow marked line Step) the largest gear step is the one from 1st to 2nd gear, which for a good speed connection and a smooth gear shift must be as small as possible A gear ratio of up to 1.6667 : 1 (5 : 3) is good Up to 1.7500 : 1 (7 : 4) is acceptable (red) Above is unsatisfactory (bold) 1 2 3 4 From large to small gears (from right to left) ↑ Standard STEP — from large to small gears: steady and progressive increase in gear steps — Gear steps should increase: Δ Step (first green highlighted line Δ Step) is always greater than 1 As progressive as possible: Δ Step is always greater than the previous step Not progressively increasing is acceptable (red) Not increasing is unsatisfactory (bold) ↑ Standard SPEED — from small to large gears: steady increase in shaft speed difference — Shaft speed differences should increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one 1 difference smaller than the previous one is acceptable (red) 2 consecutive ones are a waste of possible ratios (bold) ↑ Blocks S₁ ↑ Supports link with freewheel · blocks S₁ in one direction ↑ Blocks C₁ ↑ Couples S₁ with the input (turbine) ↑ Couples R₂ with the input (turbine) 1 2 Ordinary noted For direct determination of the gear ratio 1 2 Elementary noted Alternative representation for determining the transmission ratio Contains only operands With simple fractions of both central gears of a planetary gearset Or with the value 1 As a basis For reliable And traceable Determination of the torque conversion ratio and efficiency

References

↑ "BMWE21.net". BMWe21.net. Retrieved 24 November 2013.
↑ "ZF North America application chart (automatic)". ZF.com. Archived from the original on 22 February 2013. Retrieved 22 November 2013.

[1] Differences in gear ratios have a measurable, direct impact on vehicle dynamics, performance, waste emissions as well as fuel mileage

[Forward-2] 1 2 Forward gears only

[3] Hydraulic torque converter · German: Hydraulischer Wandler oder Drehmomentwandler

[4] Planetary gearing · German: Planetenradsätze

[5] Revised 14 January 2026
Nomenclature
$S_{n}=$ sun gear: number of teeth

$R_{n}=$ ring gear: number of teeth

$\color {gray}{C_{n}=}$ carrier or planetary gear carrier (not needed)

$s_{n}=$ sun gear: shaft speed

$r_{n}=$ ring gear: shaft speed

$c_{n}=$ carrier or planetary gear carrier: shaft speed
With $n=$ gear is
$i_{n}=$ gear ratio or transmission ratio

$\omega _{1;n}=\omega _{t}=$ shaft speed shaft 1: input (turbine) shaft

$\omega _{2;n}=$ shaft speed shaft 2: output shaft

$T_{1;n}=T_{t}=$ torque shaft 1: input (turbine) shaft

$T_{2;n}=$ torque shaft 2: output shaft

$\mu _{n}=$ torque ratio or torque conversion ratio

$\eta _{n}=$ efficiency

$i_{0}=$ stationary gear ratio

$\eta _{0}=$ (assumed) stationary gear efficiency

[mwA9M] $S_{n}=$ sun gear: number of teeth

[mwA-E] $R_{n}=$ ring gear: number of teeth

[mwA-8] $\color {gray}{C_{n}=}$ carrier or planetary gear carrier (not needed)

[mwBAA] $s_{n}=$ sun gear: shaft speed

[mwBA4] $r_{n}=$ ring gear: shaft speed

[mwBBw] $c_{n}=$ carrier or planetary gear carrier: shaft speed

[mwBDY] $i_{n}=$ gear ratio or transmission ratio

[mwBEQ] $\omega _{1;n}=\omega _{t}=$ shaft speed shaft 1: input (turbine) shaft

[mwBFk] $\omega _{2;n}=$ shaft speed shaft 2: output shaft

[mwBGk] $T_{1;n}=T_{t}=$ torque shaft 1: input (turbine) shaft

[mwBH4] $T_{2;n}=$ torque shaft 2: output shaft

[mwBI4] $\mu _{n}=$ torque ratio or torque conversion ratio

[mwBJw] $\eta _{n}=$ efficiency

[mwBKo] $i_{0}=$ stationary gear ratio

[mwBLg] $\eta _{0}=$ (assumed) stationary gear efficiency

[Gear_Ratio-6] 1 2 3 4 5 6 7 8 9 Gear ratio (transmission ratio) $i_{n}$
— speed conversion —
The gear ratio $i_{n}$ is the ratio of
input shaft speed $\omega _{1;n}$

to output shaft speed $\omega _{2;n}$

and therefore corresponds to the reciprocal of the shaft speeds
$i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}$

[mwBOw] The gear ratio $i_{n}$ is the ratio of
input shaft speed $\omega _{1;n}$

to output shaft speed $\omega _{2;n}$

[mwBPs] ut shaft speed $\omega _{1;n}$

[mwBQo] to output shaft speed $\omega _{2;n}$

[mwBRk] therefore corresponds to the reciprocal of the shaft speeds
$i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}$

[mwBRw] $i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}$

[Torque_Ratio-7] 1 2 3 4 5 6 7 8 9 Torque ratio (torque conversion ratio) $\mu _{n}$
— Torque Conversion —
The torque ratio $\mu _{n}$ is the ratio of
output torque $T_{2;n}$

to input torque $T_{1;n}$

minus efficiency losses

and therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too
$\mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}$

whereby $\eta _{n;\eta _{0}}$ may vary from gear to gear according to the formulas listed in this table and $0\leq \eta _{n;\eta _{0}}\leq 1$

[mwBXw] The torque ratio $\mu _{n}$ is the ratio of
output torque $T_{2;n}$

to input torque $T_{1;n}$

minus efficiency losses

[mwBYs] utput torque $T_{2;n}$

[mwBZo] to input torque $T_{1;n}$

[mwBak] us efficiency losses

[mwBao] therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too
$\mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}$

whereby $\eta _{n;\eta _{0}}$ may vary from gear to gear according to the formulas listed in this table and $0\leq \eta _{n;\eta _{0}}\leq 1$

[mwBa0] $\mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}$

[mwBfo] whereby $\eta _{n;\eta _{0}}$ may vary from gear to gear according to the formulas listed in this table and $0\leq \eta _{n;\eta _{0}}\leq 1$

[Efficiency-8] 1 2 3 4 5 6 7 8 Efficiency
The efficiency $\eta _{n}$ is calculated
from the torque ratio

in relation to the gear ratio (transmission ratio)

$\eta _{n}={\frac {\mu _{n}}{i_{n}}}$

Power loss for single meshing gears
is in the range of 1 % to 1.5 %

helical gear pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range

spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range
Corridor for torque ratio and efficiency
in planetary gearsets, the stationary gear ratio $i_{0}$ is formed via the planetary gears and thus by two meshes

for reasons of simplification, the efficiency for both meshes together is commonly specified there

the efficiencies $\eta _{0}$ specified here are based on assumed efficiencies for the stationary ratio $i_{0}$
of $\eta _{0}=0.9800$ (upper value)

and $\eta _{0}=0.9700$ (lower value)

for both interventions together

The corresponding efficiency
for single-meshing gear pairs is ${\eta _{0}}^{\tfrac {1}{2}}$

at $0.9800^{\tfrac {1}{2}}=0.98995$ (upper value)

and $0.9700^{\tfrac {1}{2}}=0.98489$ (lower value)

[mwBjQ] The efficiency $\eta _{n}$ is calculated
from the torque ratio

in relation to the gear ratio (transmission ratio)

$\eta _{n}={\frac {\mu _{n}}{i_{n}}}$

[mwBkM] rom the torque ratio

[mwBkQ] relation to the gear ratio (transmission ratio)

[mwBkU] $\eta _{n}={\frac {\mu _{n}}{i_{n}}}$

[mwBl0] Power loss for single meshing gears
is in the range of 1 % to 1.5 %

helical gear pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range

spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range

[mwBl8] s in the range of 1 % to 1.5 %

[mwBmI] r pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range

[mwBmM] spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range

[mwBmc] tary gearsets, the stationary gear ratio $i_{0}$ is formed via the planetary gears and thus by two meshes

[mwBnU] r reasons of simplification, the efficiency for both meshes together is commonly specified there

[mwBnY] the efficiencies $\eta _{0}$ specified here are based on assumed efficiencies for the stationary ratio $i_{0}$
of $\eta _{0}=0.9800$ (upper value)

and $\eta _{0}=0.9700$ (lower value)

[mwBpE] $\eta _{0}=0.9800$ (upper value)

[mwBqA] $\eta _{0}=0.9700$ (lower value)

[mwBq8] r both interventions together

[mwBrA] The corresponding efficiency
for single-meshing gear pairs is ${\eta _{0}}^{\tfrac {1}{2}}$

at $0.9800^{\tfrac {1}{2}}=0.98995$ (upper value)

and $0.9700^{\tfrac {1}{2}}=0.98489$ (lower value)

[mwBrI] r single-meshing gear pairs is ${\eta _{0}}^{\tfrac {1}{2}}$

[mwBsY] t $0.9800^{\tfrac {1}{2}}=0.98995$ (upper value)

[mwBtg] $0.9700^{\tfrac {1}{2}}=0.98489$ (lower value)

[9] Layout
Input and output are on opposite sides

Planetary gearset 2 (the outer Ravigneaux gearset) is on the input (turbine) side

Input (turbine) shafts is, if actuated S₁ or S₂

Output shaft is R₂ (ring gear of the outer Ravigneaux gearset)

[mwBu8] Input and output are on opposite sides

[mwBvA] Planetary gearset 2 (the outer Ravigneaux gearset) is on the input (turbine) side

[mwBvE] Input (turbine) shafts is, if actuated S₁ or S₂

[mwBvY] Output shaft is R₂ (ring gear of the outer Ravigneaux gearset)

[10] Total ratio span (total gear ratio/total transmission ratio) nominal
${\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}$

A wider span enables the
downspeeding when driving outside the city limits

increase the climbing ability
when driving over mountain passes or off-road

or when towing a trailer

[mwBv4] ${\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}$

[mwB3c] A wider span enables the
downspeeding when driving outside the city limits

increase the climbing ability
when driving over mountain passes or off-road

or when towing a trailer

[mwB3k] wnspeeding when driving outside the city limits

[mwB3o] rease the climbing ability
when driving over mountain passes or off-road

or when towing a trailer

[mwB3w] when driving over mountain passes or off-road

[mwB30] r when towing a trailer

[effective-11] 1 2 3 4 5 Total ratio span (total gear ratio/total transmission ratio) effective
${\frac {\omega _{2;n}}{max(\omega _{2;1};|\omega _{2;R}|)}}={\frac {min(i_{1};|i_{R}|)}{i_{n}}}$

The span is only effective to the extent that
the reverse gear ratio

matches that of 1st gear

see also Standard R:1
Digression
Reverse gear
is usually longer than 1st gear

the effective span is therefore of central importance for describing the suitability of a transmission

because in these cases, the nominal spread conveys a misleading picture

which is only unproblematic for vehicles with high specific power
Market participants
Manufacturers naturally have no interest in specifying the effective span

Users have not yet formulated the practical benefits that the effective span has for them

The effective span has not yet played a role in research and teaching
Contrary to its significance
the effective span has therefore not yet been able to establish itself
either in theory

or in practice.
End of digression

[mwB4s] ${\frac {\omega _{2;n}}{max(\omega _{2;1};|\omega _{2;R}|)}}={\frac {min(i_{1};|i_{R}|)}{i_{n}}}$

[mwB80] The span is only effective to the extent that
the reverse gear ratio

matches that of 1st gear

[mwB88] the reverse gear ratio

[mwB9A] tches that of 1st gear

[mwB9E] see also Standard R:1

[mwB9c] s usually longer than 1st gear

[mwB9o] the effective span is therefore of central importance for describing the suitability of a transmission

[mwB94] use in these cases, the nominal spread conveys a misleading picture

[mwB-E] which is only unproblematic for vehicles with high specific power

[mwB-Y] Manufacturers naturally have no interest in specifying the effective span

[mwB-g] Users have not yet formulated the practical benefits that the effective span has for them

[mwB-o] The effective span has not yet played a role in research and teaching

[mwB-8] the effective span has therefore not yet been able to establish itself
either in theory

or in practice.

[mwB_Q] ther in theory

[mwB_c] r in practice.

[12] Ratio span's center
$(i_{1}i_{n})^{\frac {1}{2}}$

The center indicates the speed level of the transmission

Together with the final drive ratio

it gives the shaft speed level of the vehicle

[mwCAI] $(i_{1}i_{n})^{\frac {1}{2}}$

[mwCBo] The center indicates the speed level of the transmission

[mwCBs] Together with the final drive ratio

[mwCBw] t gives the shaft speed level of the vehicle

[13] Average gear step
$\left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}$

There are $n-1$ gear steps between $n$ gears

with decreasing step width
the gears connect better to each other

shifting comfort increases

[mwCCI] $\left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}$

[mwCFo] There are $n-1$ gear steps between $n$ gears

[mwCG8] with decreasing step width
the gears connect better to each other

shifting comfort increases

[mwCHE] the gears connect better to each other

[mwCHI] shifting comfort increases

[14] Sun 1: sun gear of gearset 1: inner Ravigneaux gearset

[15] Ring 1: ring gear of gearset 1: inner Ravigneaux gearset

[16] Sun 2: sun gear of gearset 2: outer Ravigneaux gearset

[17] Ring 2: ring gear of gearset 2: outer Ravigneaux gearset

[50:50-18] 1 2 3 4 Standard 50:50
— 50 % is above and 50 % is below the average gear step —
With steadily decreasing gear steps (yellow highlighted line Step)

and a particularly large step from 1st to 2nd gear
the lower half of the gear steps (between the small gears; rounded down, here the first 1) is always larger

and the upper half of the gear steps (between the large gears; rounded up, here the last 1) is always smaller

than the average gear step (cell highlighted yellow two rows above on the far right)

lower half: smaller gear steps are a waste of possible ratios (red bold)

upper half: larger gear steps are unsatisfactory (red bold)

[mwCJI] With steadily decreasing gear steps (yellow highlighted line Step)

[mwCJQ] rticularly large step from 1st to 2nd gear
the lower half of the gear steps (between the small gears; rounded down, here the first 1) is always larger

and the upper half of the gear steps (between the large gears; rounded up, here the last 1) is always smaller

[mwCJY] the lower half of the gear steps (between the small gears; rounded down, here the first 1) is always larger

[mwCJk] the upper half of the gear steps (between the large gears; rounded up, here the last 1) is always smaller

[mwCJw] than the average gear step (cell highlighted yellow two rows above on the far right)

[mwCJ4] wer half: smaller gear steps are a waste of possible ratios (red bold)

[mwCKI] upper half: larger gear steps are unsatisfactory (red bold)

[R:1-19] 1 2 3 4 5 6 7 Standard R:1
— reverse and 1st gear have the same ratio —
The ideal reverse gear has the same transmission ratio as 1st gear
no impairment when maneuvering

especially when towing a trailer

a torque converter can only partially compensate for this deficiency

Plus 11.11 % minus 10 % compared to 1st gear is good

Plus 25 % minus 20 % is acceptable (red)

Above this is unsatisfactory (bold)

see also Total ratio span (total gear ratio/total transmission ratio) effective

[mwCL0] The ideal reverse gear has the same transmission ratio as 1st gear
no impairment when maneuvering

especially when towing a trailer

a torque converter can only partially compensate for this deficiency

[mwCL8] rment when maneuvering

[mwCMA] specially when towing a trailer

[mwCME] torque converter can only partially compensate for this deficiency

[mwCMI] Plus 11.11 % minus 10 % compared to 1st gear is good

[mwCMU] Plus 25 % minus 20 % is acceptable (red)

[mwCMk] Above this is unsatisfactory (bold)

[mwCMw] see also Total ratio span (total gear ratio/total transmission ratio) effective

[1:2-20] 1 2 3 Standard 1:2
— gear step 1st to 2nd gear as small as possible —
With continuously decreasing gear steps (yellow marked line Step)

the largest gear step is the one from 1st to 2nd gear, which
for a good speed connection and

a smooth gear shift

must be as small as possible
A gear ratio of up to 1.6667 : 1 (5 : 3) is good

Up to 1.7500 : 1 (7 : 4) is acceptable (red)

Above is unsatisfactory (bold)

[mwCN0] With continuously decreasing gear steps (yellow marked line Step)

[mwCN8] the largest gear step is the one from 1st to 2nd gear, which
for a good speed connection and

a smooth gear shift

[mwCOI] r a good speed connection and

[mwCOM] smooth gear shift

[mwCOQ] ust be as small as possible
A gear ratio of up to 1.6667 : 1 (5 : 3) is good

Up to 1.7500 : 1 (7 : 4) is acceptable (red)

Above is unsatisfactory (bold)

[mwCOY] A gear ratio of up to 1.6667 : 1 (5 : 3) is good

[mwCOk] Up to 1.7500 : 1 (7 : 4) is acceptable (red)

[mwCO0] Above is unsatisfactory (bold)

[LS-21] 1 2 3 From large to small gears (from right to left)

[step-22] Standard STEP
— from large to small gears: steady and progressive increase in gear steps —
Gear steps should
increase: Δ Step (first green highlighted line Δ Step) is always greater than 1

As progressive as possible: Δ Step is always greater than the previous step

Not progressively increasing is acceptable (red)

Not increasing is unsatisfactory (bold)

[mwCQI] Gear steps should
increase: Δ Step (first green highlighted line Δ Step) is always greater than 1

As progressive as possible: Δ Step is always greater than the previous step

[mwCQQ] increase: Δ Step (first green highlighted line Δ Step) is always greater than 1

[mwCQk] As progressive as possible: Δ Step is always greater than the previous step

[mwCQw] Not progressively increasing is acceptable (red)

[mwCQ4] Not increasing is unsatisfactory (bold)

[speed-23] Standard SPEED
— from small to large gears: steady increase in shaft speed difference —
Shaft speed differences should
increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one

1 difference smaller than the previous one is acceptable (red)

2 consecutive ones are a waste of possible ratios (bold)

[mwCRw] Shaft speed differences should
increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one

[mwCR4] increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one

[mwCSM] 1 difference smaller than the previous one is acceptable (red)

[mwCSU] 2 consecutive ones are a waste of possible ratios (bold)

[24] Blocks R₁ (ring gear of the inner Ravigneaux gearset) and S₂ (sun gear of the outer Ravigneaux gearset)

[25] Supports link with freewheel · blocks R₁ (ring gear of the inner Ravigneaux gearset) and S₂ (sun gear of the outer Ravigneaux gearset) in one direction

[26] Blocks C₁ and C₂ (the common carrier of the compound Ravigneaux gearset)

[27] Couples S₁ (sun gear of the inner Ravigneaux gearset) with the input (turbine)

[28] Couples S₂ (sun gear of the outer Ravigneaux gearset) with the input (turbine)

[ordinary-29] Ordinary noted
For direct determination of the ratio

[mwCUw] For direct determination of the ratio

[elementary-30] Elementary noted
Alternative representation for determining the transmission ratio

Contains only operands
With simple fractions of both central gears of a planetary gearset

Or with the value 1

As a basis
For reliable

And traceable

Determination of specific torque and efficiency

[mwCVI] Alternative representation for determining the transmission ratio

[mwCVM] Contains only operands
With simple fractions of both central gears of a planetary gearset

Or with the value 1

[mwCVU] With simple fractions of both central gears of a planetary gearset

[mwCVY] Or with the value 1

[mwCVc] As a basis
For reliable

And traceable

[mwCVk] For reliable

[mwCVo] And traceable

[mwCVs] Determination of specific torque and efficiency

[33] Revised 14 January 2026
Nomenclature
$S_{n}=$ sun gear: number of teeth

$R_{n}=$ ring gear: number of teeth

$\color {gray}{C_{n}=}$ carrier or planetary gear carrier (not needed)

$s_{n}=$ sun gear: shaft speed

$r_{n}=$ ring gear: shaft speed

$c_{n}=$ carrier or planetary gear carrier: shaft speed
With $n=$ gear is
$i_{n}=$ gear ratio or transmission ratio

$\omega _{1;n}=\omega _{t}=$ shaft speed shaft 1: input (turbine) shaft

$\omega _{2;n}=$ shaft speed shaft 2: output shaft

$T_{1;n}=T_{t}=$ torque shaft 1: input (turbine) shaft

$T_{2;n}=$ torque shaft 2: output shaft

$\mu _{n}=$ torque ratio or torque conversion ratio

$\eta _{n}=$ efficiency

$i_{0}=$ stationary gear ratio

$\eta _{0}=$ (assumed) stationary gear efficiency

[mwDRc] $S_{n}=$ sun gear: number of teeth

[mwDSU] $R_{n}=$ ring gear: number of teeth

[mwDTM] $\color {gray}{C_{n}=}$ carrier or planetary gear carrier (not needed)

[mwDUQ] $s_{n}=$ sun gear: shaft speed

[mwDVI] $r_{n}=$ ring gear: shaft speed

[mwDWA] $c_{n}=$ carrier or planetary gear carrier: shaft speed

[mwDXo] $i_{n}=$ gear ratio or transmission ratio

[mwDYg] $\omega _{1;n}=\omega _{t}=$ shaft speed shaft 1: input (turbine) shaft

[mwDZ0] $\omega _{2;n}=$ shaft speed shaft 2: output shaft

[mwDa0] $T_{1;n}=T_{t}=$ torque shaft 1: input (turbine) shaft

[mwDcI] $T_{2;n}=$ torque shaft 2: output shaft

[mwDdI] $\mu _{n}=$ torque ratio or torque conversion ratio

[mwDeA] $\eta _{n}=$ efficiency

[mwDe4] $i_{0}=$ stationary gear ratio

[mwDfw] $\eta _{0}=$ (assumed) stationary gear efficiency

[Gear_Ratio-34] 1 2 3 4 5 6 7 8 9 10 11 Gear ratio (transmission ratio) $i_{n}$
— speed conversion —
The gear ratio $i_{n}$ is the ratio of
input shaft speed $\omega _{1;n}$

to output shaft speed $\omega _{2;n}$

and therefore corresponds to the reciprocal of the shaft speeds
$i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}$

[mwDjQ] The gear ratio $i_{n}$ is the ratio of
input shaft speed $\omega _{1;n}$

to output shaft speed $\omega _{2;n}$

[mwDkM] ut shaft speed $\omega _{1;n}$

[mwDlI] to output shaft speed $\omega _{2;n}$

[mwDmE] therefore corresponds to the reciprocal of the shaft speeds
$i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}$

[mwDmQ] $i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}$

[Torque_Ratio-35] 1 2 3 4 5 6 7 8 9 10 11 Torque ratio (torque conversion ratio) $\mu _{n}$
— torque conversion —
The torque ratio $\mu _{n}$ is the ratio of
output torque $T_{2;n}$

to input torque $T_{1;n}$

minus efficiency losses

and therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too
$\mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}$

whereby $\eta _{n;\eta _{0}}$ may vary from gear to gear according to the formulas listed in this table and $0\leq \eta _{n;\eta _{0}}\leq 1$

[mwDsg] The torque ratio $\mu _{n}$ is the ratio of
output torque $T_{2;n}$

to input torque $T_{1;n}$

minus efficiency losses

[mwDtc] utput torque $T_{2;n}$

[mwDuY] to input torque $T_{1;n}$

[mwDvU] us efficiency losses

[mwDvY] therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too
$\mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}$

whereby $\eta _{n;\eta _{0}}$ may vary from gear to gear according to the formulas listed in this table and $0\leq \eta _{n;\eta _{0}}\leq 1$

[mwDvk] $\mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}$

[mwD0Y] whereby $\eta _{n;\eta _{0}}$ may vary from gear to gear according to the formulas listed in this table and $0\leq \eta _{n;\eta _{0}}\leq 1$

[Efficiency-36] 1 2 3 4 5 6 7 8 9 Efficiency
The efficiency $\eta _{n}$ is calculated
from the torque ratio

in relation to the gear ratio (transmission ratio)

$\eta _{n}={\frac {\mu _{n}}{i_{n}}}$

Power loss for single meshing gears
is in the range of 1 % to 1.5 %

helical gear pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range

spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range
Corridor for torque ratio and efficiency
in planetary gearsets, the stationary gear ratio $i_{0}$ is formed via the planetary gears and thus by two meshes

for reasons of simplification, the efficiency for both meshes together is commonly specified there

the efficiencies $\eta _{0}$ specified here are based on assumed efficiencies for the stationary ratio $i_{0}$
of $\eta _{0}=0.9800$ (upper value)

and $\eta _{0}=0.9700$ (lower value)

for both interventions together

The corresponding efficiency
for single-meshing gear pairs is ${\eta _{0}}^{\tfrac {1}{2}}$

at $0.9800^{\tfrac {1}{2}}=0.98995$ (upper value)

and $0.9700^{\tfrac {1}{2}}=0.98489$ (lower value)

[mwD4I] The efficiency $\eta _{n}$ is calculated
from the torque ratio

in relation to the gear ratio (transmission ratio)

$\eta _{n}={\frac {\mu _{n}}{i_{n}}}$

[mwD5E] rom the torque ratio

[mwD5I] relation to the gear ratio (transmission ratio)

[mwD5M] $\eta _{n}={\frac {\mu _{n}}{i_{n}}}$

[mwD6s] Power loss for single meshing gears
is in the range of 1 % to 1.5 %

helical gear pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range

spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range

[mwD60] s in the range of 1 % to 1.5 %

[mwD7A] r pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range

[mwD7E] spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range

[mwD7U] tary gearsets, the stationary gear ratio $i_{0}$ is formed via the planetary gears and thus by two meshes

[mwD8M] r reasons of simplification, the efficiency for both meshes together is commonly specified there

[mwD8Q] the efficiencies $\eta _{0}$ specified here are based on assumed efficiencies for the stationary ratio $i_{0}$
of $\eta _{0}=0.9800$ (upper value)

and $\eta _{0}=0.9700$ (lower value)

[mwD98] $\eta _{0}=0.9800$ (upper value)

[mwD-4] $\eta _{0}=0.9700$ (lower value)

[mwD_0] r both interventions together

[mwD_4] The corresponding efficiency
for single-meshing gear pairs is ${\eta _{0}}^{\tfrac {1}{2}}$

at $0.9800^{\tfrac {1}{2}}=0.98995$ (upper value)

and $0.9700^{\tfrac {1}{2}}=0.98489$ (lower value)

[mwEAA] r single-meshing gear pairs is ${\eta _{0}}^{\tfrac {1}{2}}$

[mwEBQ] t $0.9800^{\tfrac {1}{2}}=0.98995$ (upper value)

[mwECY] $0.9700^{\tfrac {1}{2}}=0.98489$ (lower value)

[37] Layout
Input and output are on opposite sides

Planetary gearset 1 is on the input (turbine) side

Input (turbine) shaft is, if actuated, S₁ or R₂

Output shaft is R₁

[mwED0] Input and output are on opposite sides

[mwED4] Planetary gearset 1 is on the input (turbine) side

[mwED8] Input (turbine) shaft is, if actuated, S₁ or R₂

[mwEEQ] Output shaft is R₁

[38] Total ratio span (total gear ratio/total transmission ratio) nominal
${\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}$

A wider span enables the
downspeeding when driving outside the city limits

increase the climbing ability
when driving over mountain passes or off-road

or when towing a trailer

[mwEEw] ${\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}$

[mwEMU] A wider span enables the
downspeeding when driving outside the city limits

increase the climbing ability
when driving over mountain passes or off-road

or when towing a trailer

[mwEMc] wnspeeding when driving outside the city limits

[mwEMg] rease the climbing ability
when driving over mountain passes or off-road

or when towing a trailer

[mwEMo] when driving over mountain passes or off-road

[mwEMs] r when towing a trailer

[effective-39] 1 2 3 4 5 6 7 Total ratio span (total gear ratio/total transmission ratio) effective
${\frac {\omega _{2;n}}{max(\omega _{2;1};|\omega _{2;R}|)}}={\frac {min(i_{1};|i_{R}|)}{i_{n}}}$

The span is only effective to the extent that
the reverse gear ratio

matches that of 1st gear

see also Standard R:1
Digression
Reverse gear
is usually longer than 1st gear

the effective span is therefore of central importance for describing the suitability of a transmission

because in these cases, the nominal spread conveys a misleading picture

which is only unproblematic for vehicles with high specific power
Market participants
Manufacturers naturally have no interest in specifying the effective span

Users have not yet formulated the practical benefits that the effective span has for them

The effective span has not yet played a role in research and teaching
Contrary to its significance
the effective span has therefore not yet been able to establish itself
either in theory

or in practice.
End of digression

[mwEN0] ${\frac {\omega _{2;n}}{max(\omega _{2;1};|\omega _{2;R}|)}}={\frac {min(i_{1};|i_{R}|)}{i_{n}}}$

[mwER8] The span is only effective to the extent that
the reverse gear ratio

matches that of 1st gear

[mwESE] the reverse gear ratio

[mwESI] tches that of 1st gear

[mwESM] see also Standard R:1

[mwESk] s usually longer than 1st gear

[mwESw] the effective span is therefore of central importance for describing the suitability of a transmission

[mwETA] use in these cases, the nominal spread conveys a misleading picture

[mwETM] which is only unproblematic for vehicles with high specific power

[mwETg] Manufacturers naturally have no interest in specifying the effective span

[mwETo] Users have not yet formulated the practical benefits that the effective span has for them

[mwETw] The effective span has not yet played a role in research and teaching

[mwEUE] the effective span has therefore not yet been able to establish itself
either in theory

or in practice.

[mwEUY] ther in theory

[mwEUk] r in practice.

[40] Ratio span's center
$(i_{1}i_{n})^{\frac {1}{2}}$

The center indicates the speed level of the transmission

Together with the final drive ratio

it gives the shaft speed level of the vehicle

[mwEVQ] $(i_{1}i_{n})^{\frac {1}{2}}$

[mwEWw] The center indicates the speed level of the transmission

[mwEW0] Together with the final drive ratio

[mwEW4] t gives the shaft speed level of the vehicle

[41] Average gear step
$\left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}$

There are $n-1$ gear steps between $n$ gears

with decreasing step width
the gears connect better to each other

shifting comfort increases

[mwEXQ] $\left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}$

[mwEaw] There are $n-1$ gear steps between $n$ gears

[mwEcE] with decreasing step width
the gears connect better to each other

shifting comfort increases

[mwEcM] the gears connect better to each other

[mwEcQ] shifting comfort increases

[42] Sun 1: sun gear of gearset 1: inner Ravigneaux gearset

[43] Ring 1: ring gear of gearset 1: inner Ravigneaux gearset

[44] Sun 2: sun gear of gearset 2: outer Ravigneaux gearset

[45] Ring 2: ring gear of gearset 2: outer Ravigneaux gearset

[50:50-46] 1 2 3 4 5 Standard 50:50
— 50 % is above and 50 % is below the average gear step —
With steadily decreasing gear steps (yellow highlighted line Step)

and a particularly large step from 1st to 2nd gear
the lower half of the gear steps (between the small gears; rounded down, here the first 1) is always larger

and the upper half of the gear steps (between the large gears; rounded up, here the last 1) is always smaller

than the average gear step (cell highlighted yellow two rows above on the far right)

lower half: smaller gear steps are a waste of possible ratios (red bold)

upper half: larger gear steps are unsatisfactory (red bold)

[mwEeY] With steadily decreasing gear steps (yellow highlighted line Step)

[mwEeg] rticularly large step from 1st to 2nd gear
the lower half of the gear steps (between the small gears; rounded down, here the first 1) is always larger

and the upper half of the gear steps (between the large gears; rounded up, here the last 1) is always smaller

[mwEeo] the lower half of the gear steps (between the small gears; rounded down, here the first 1) is always larger

[mwEe0] the upper half of the gear steps (between the large gears; rounded up, here the last 1) is always smaller

[mwEfA] than the average gear step (cell highlighted yellow two rows above on the far right)

[mwEfI] wer half: smaller gear steps are a waste of possible ratios (red bold)

[mwEfY] upper half: larger gear steps are unsatisfactory (red bold)

[R:1-47] 1 2 3 4 5 6 7 8 9 10 Standard R:1
— reverse and 1st gear have the same ratio —
The ideal reverse gear has the same transmission ratio as 1st gear
no impairment when maneuvering

especially when towing a trailer

a torque converter can only partially compensate for this deficiency

Plus 11.11 % minus 10 % compared to 1st gear is good

Plus 25 % minus 20 % is acceptable (red)

Above this is unsatisfactory (bold)

see also Total ratio span (total gear ratio/total transmission ratio) effective

[mwEhc] The ideal reverse gear has the same transmission ratio as 1st gear
no impairment when maneuvering

especially when towing a trailer

a torque converter can only partially compensate for this deficiency

[mwEhk] rment when maneuvering

[mwEho] specially when towing a trailer

[mwEhs] torque converter can only partially compensate for this deficiency

[mwEhw] Plus 11.11 % minus 10 % compared to 1st gear is good

[mwEh8] Plus 25 % minus 20 % is acceptable (red)

[mwEiM] Above this is unsatisfactory (bold)

[mwEiY] see also Total ratio span (total gear ratio/total transmission ratio) effective

[1:2-48] 1 2 3 4 5 6 7 Standard 1:2
— gear step 1st to 2nd gear as small as possible —
With continuously decreasing gear steps (yellow marked line Step)

the largest gear step is the one from 1st to 2nd gear, which
for a good speed connection and

a smooth gear shift

must be as small as possible
A gear ratio of up to 1.6667 : 1 (5 : 3) is good

Up to 1.7500 : 1 (7 : 4) is acceptable (red)

Above is unsatisfactory (bold)

[mwEj8] With continuously decreasing gear steps (yellow marked line Step)

[mwEkE] the largest gear step is the one from 1st to 2nd gear, which
for a good speed connection and

a smooth gear shift

[mwEkQ] r a good speed connection and

[mwEkU] smooth gear shift

[mwEkY] ust be as small as possible
A gear ratio of up to 1.6667 : 1 (5 : 3) is good

Up to 1.7500 : 1 (7 : 4) is acceptable (red)

Above is unsatisfactory (bold)

[mwEkg] A gear ratio of up to 1.6667 : 1 (5 : 3) is good

[mwEks] Up to 1.7500 : 1 (7 : 4) is acceptable (red)

[mwEk8] Above is unsatisfactory (bold)

[LS-49] 1 2 3 4 From large to small gears (from right to left)

[step-50] Standard STEP
— from large to small gears: steady and progressive increase in gear steps —
Gear steps should
increase: Δ Step (first green highlighted line Δ Step) is always greater than 1

As progressive as possible: Δ Step is always greater than the previous step

Not progressively increasing is acceptable (red)

Not increasing is unsatisfactory (bold)

[mwEmY] Gear steps should
increase: Δ Step (first green highlighted line Δ Step) is always greater than 1

As progressive as possible: Δ Step is always greater than the previous step

[mwEmg] increase: Δ Step (first green highlighted line Δ Step) is always greater than 1

[mwEm0] As progressive as possible: Δ Step is always greater than the previous step

[mwEnA] Not progressively increasing is acceptable (red)

[mwEnI] Not increasing is unsatisfactory (bold)

[speed-51] Standard SPEED
— from small to large gears: steady increase in shaft speed difference —
Shaft speed differences should
increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one

1 difference smaller than the previous one is acceptable (red)

2 consecutive ones are a waste of possible ratios (bold)

[mwEoA] Shaft speed differences should
increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one

[mwEoI] increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one

[mwEoc] 1 difference smaller than the previous one is acceptable (red)

[mwEok] 2 consecutive ones are a waste of possible ratios (bold)

[52] Blocks S₁

[53] Supports link with freewheel · blocks S₁ in one direction

[54] Blocks C₁

[55] Couples S₁ with the input (turbine)

[56] Couples R₂ with the input (turbine)

[ordinary-57] 1 2 Ordinary noted
For direct determination of the gear ratio

[mwEqw] For direct determination of the gear ratio

[elementary-58] 1 2 Elementary noted
Alternative representation for determining the transmission ratio

Contains only operands
With simple fractions of both central gears of a planetary gearset

Or with the value 1

As a basis
For reliable

And traceable

Determination of the torque conversion ratio and efficiency

[mwErQ] Alternative representation for determining the transmission ratio

[mwErU] Contains only operands
With simple fractions of both central gears of a planetary gearset

Or with the value 1

[mwErc] With simple fractions of both central gears of a planetary gearset

[mwErg] Or with the value 1

[mwErk] As a basis
For reliable

And traceable

[mwErs] For reliable

[mwErw] And traceable

[mwEr0] Determination of the torque conversion ratio and efficiency

[31] "BMWE21.net". BMWe21.net. Retrieved 24 November 2013.

[32] "ZF North America application chart (automatic)". ZF.com. Archived from the original on 22 February 2013. Retrieved 22 November 2013.

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Key data

1963: 3HP 12— Ravigneaux planetary gearset types —

History

Planetary gearset concept

1973: 3HP 22— Simpson planetary gearset types —

History

Specifications

Planetary gearset concept

See also

References

1963: 3HP 12
— Ravigneaux planetary gearset types —

1973: 3HP 22
— Simpson planetary gearset types —