Mercedes-Benz 4G-Tronic transmission

Basic Concept

The 4G-Tronic transmission is a hydraulically operated 4-speed automatic without lock-up that replaced the similarly designed W3A 040, W3B 050, and W4B 025 family of automatic transmissions with the introduction of the W126 S-Class in 1979. In some models it is calibrated to move off in second gear to reduce "creeping" and provide a smoother ride, selecting 1st only if the selector is in "2" or in case of abrupt acceleration. Other calibrations have the transmission rest in 2nd gear and kick down to 1st as soon as the accelerator is touched but before the throttle is opened. In some V8 installations a small control unit activates the kick down solenoid when the brake pedal is released so that the car moves off in 1st gear. Other attributes of this transmission include a 2-3 shift delay when the engine is cold in order to speed up catalyst warm-up. 4th gear is a 1:1 ratio. Controls are all mechanical and pneumatic, except for the kickdown solenoid and 2-3 upshift delay solenoid on some models.

In some markets a W-S (Winter - Standard / Sport) switch was provided on the shifter. Activating S mode changes a linkage which effectively shortens the throttle pressure bowden cable. This causes later, higher RPM shifts and on some models a move off in 1st gear instead of 2nd. On V8 models a B (Brake) range is available on the shifter. This activates the kickdown solenoid, forcing the transmission to shift down to 1st sooner for increased engine braking. A hydraulically activated piston prevents shifting into Reverse when the car is moving forward.

Models from 1990 and earlier allow for push starting the engine. They are fitted with a secondary fluid pump, driven by the transmission output shaft. When the vehicle is rolling at 20 mph shifting from Neutral to the 2 range will couple power to the engine. The secondary pump and thus the push starting facility was eliminated for the 1991 model year.

It is considered by enthusiasts to be one of the most reliable transmissions ever built by Mercedes-Benz with some examples exceeding 300,000 miles of service.

Gearset Concept W4A Models: Cost Effectiveness

"To simplify production, the front group is now formed by a Ravigneaux set, which is immediately followed by the second group. This largely eliminates the need for hollow shafts and other connecting bells, which are so commonly found in planetary gearboxes. Where possible, sheet metal or die-cast parts are used. Cost-intensive material machining is limited to the manufacture of gears, shafts, and bolts."^[A]

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Gearset Concept: Cost-Effectiveness^[a]

With Assessment	Output: Gear Ratios	Innovation Elasticity[b] Δ Output : Δ Input	Input: Main Components
			Total	Gearsets	Brakes	Clutches
W4A Ref. Object	${\displaystyle n_{O1}}$ ${\displaystyle n_{O2}}$	Topic[b]	${\displaystyle n_{I}=n_{G}+}$ ${\displaystyle n_{B}+n_{C}}$	${\displaystyle n_{G1}}$ ${\displaystyle n_{G2}}$	${\displaystyle n_{B1}}$ ${\displaystyle n_{B2}}$	${\displaystyle n_{C1}}$ ${\displaystyle n_{C2}}$
Δ Number	${\displaystyle n_{O1}-n_{O2}}$		${\displaystyle n_{I1}-n_{I2}}$	${\displaystyle n_{G1}-n_{G2}}$	${\displaystyle n_{B1}-n_{B2}}$	${\displaystyle n_{C1}-n_{C2}}$
Relative Δ	Δ Output ${\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}}$	${\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}:{\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}$ ${\displaystyle ={\tfrac {n_{O1}-n_{O2}}{n_{O2}}}\cdot {\tfrac {n_{I2}}{n_{I1}-n_{I2}}}}$	Δ Input ${\displaystyle {\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}$	${\displaystyle {\tfrac {n_{G1}-n_{G2}}{n_{G2}}}}$	${\displaystyle {\tfrac {n_{B1}-n_{B2}}{n_{B2}}}}$	${\displaystyle {\tfrac {n_{C1}-n_{C2}}{n_{C2}}}}$
W4A W4B 025[c]	4[d] 4[d]	Progress[b]	8 8	3[e] 3	3 3	2 2
Δ Number	0		0	0	0	0
Relative Δ	0.000 ${\displaystyle {\tfrac {0}{4}}}$	0.000[b] ${\displaystyle {\tfrac {0}{4}}:{\tfrac {0}{8}}={\tfrac {0}{4}}\cdot {\tfrac {8}{0}}={\tfrac {0}{0}}}$	0.000 ${\displaystyle {\tfrac {0}{8}}}$	0.000 ${\displaystyle {\tfrac {0}{3}}}$	0.000 ${\displaystyle {\tfrac {0}{3}}}$	0.000 ${\displaystyle {\tfrac {0}{2}}}$
W4A ZF 4HP 22	4[d] 4[d]	Early Market Position[b]	8 10	3[e] 3	3 4	2 3
Δ Number	0		-2	0	-1	-1
Relative Δ	0.000 ${\displaystyle {\tfrac {0}{4}}}$	0.000[b] ${\displaystyle {\tfrac {0}{4}}:{\tfrac {-2}{10}}={\tfrac {0}{4}}\cdot {\tfrac {10}{-2}}={\tfrac {0}{-8}}}$	−0.200 ${\displaystyle {\tfrac {-2}{10}}}$	0.000 ${\displaystyle {\tfrac {0}{3}}}$	−0.250 ${\displaystyle {\tfrac {-1}{4}}}$	−0.333 ${\displaystyle {\tfrac {-1}{3}}}$
W4A ZF 4HP 18	4[d] 4[d]	Late Market Position[b]	8 7	3[e] 2[e]	3 2	2 3
Δ Number	0		1	1	1	-1
Relative Δ	0.000 ${\displaystyle {\tfrac {0}{4}}}$	0.000[b] ${\displaystyle {\tfrac {0}{4}}:{\tfrac {1}{7}}={\tfrac {0}{4}}\cdot {\tfrac {7}{1}}={\tfrac {0}{4}}}$	0.143 ${\displaystyle {\tfrac {1}{7}}}$	0.500 ${\displaystyle {\tfrac {1}{2}}}$	0.500 ${\displaystyle {\tfrac {1}{2}}}$	−0.333 ${\displaystyle {\tfrac {-1}{3}}}$
W4A 3-Speed[f]	4[d] 3[d]	Historical Market Position[b]	8 7	3[e] 2	3 3	2 2
Δ Number	1		1	1	0	0
Relative Δ	0.333 ${\displaystyle {\tfrac {1}{3}}}$	2.333[b] ${\displaystyle {\tfrac {1}{3}}:{\tfrac {1}{7}}={\tfrac {1}{3}}\cdot {\tfrac {7}{1}}={\tfrac {7}{3}}}$	0.143 ${\displaystyle {\tfrac {1}{7}}}$	0.500 ${\displaystyle {\tfrac {1}{2}}}$	0.000 ${\displaystyle {\tfrac {0}{3}}}$	0.000 ${\displaystyle {\tfrac {0}{2}}}$
[a] Progress increases cost-effectiveness and is reflected in the ratio of forward gears to main components. It depends on the power flow: parallel: using the two degrees of freedom of planetary gearsets to increase the number of gears with unchanged number of components serial: in-line combined planetary gearsets without using the two degrees of freedom to increase the number of gears a corresponding increase in the number of components is unavoidable [b] Innovation Elasticity Classifies Progress And Market Position Automobile manufacturers drive forward technical developments primarily in order to remain competitive or to achieve or defend technological leadership. This technical progress has therefore always been subject to economic constraints Only innovations whose relative additional benefit is greater than the relative additional resource input, i.e. whose economic elasticity is greater than 1, are considered for realization The required innovation elasticity of an automobile manufacturer depends on its expected return on investment. The basic assumption that the relative additional benefit must be at least twice as high as the relative additional resource input helps with orientation negative, if the output increases and the input decreases, is perfect 2 or above is good 1 or above is acceptable (red) below this is unsatisfactory (bold) [c] Direct Predecessor To reflect the progress of the specific model change [d] plus 1 reverse gear [e] of which 2 gearsets are combined as a compound Ravigneaux gearset [f] Historical Reference Standard (Benchmark) 3-speed transmissions with torque converters have established the modern market for automatic transmissions and thus made it possible in the first place, as this design proved to be a particularly successful compromise between cost and performance It became the archetype and dominated the world market for around 3 decades, setting the standard for automatic transmissions. It was only when fuel consumption became the focus of interest that this design reached its limits, which is why it has now completely disappeared from the market What has remained is the orientation that it offers as a reference standard (point of reference, benchmark) for this market for determining progressiveness and thus the market position of all other, later designs All transmission variants consist of 7 main components Typical examples are Turbo-Hydramatic from GM Cruise-O-Matic from Ford TorqueFlite from Chrysler Detroit Gear from BorgWarner for Studebaker BW-35 from BorgWarner and as T35 from Aisin 3N 71 from Nissan/Jatco 3 HP from ZF Friedrichshafen W3A 040 and W3B 050 from Mercedes-Benz

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Gearset Concept W5A: Cost Effectiveness

The need of 2 housings^[a] and 2 different controls^[b] turn out the W5A 030 as the least economically designed automatic transmission ever manufactured for passenger cars. Obviously a transition solution: the direct successor, launched in 1996, requires 9 main components,^[c] 1 housing and 1 control.^[d]

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Gearset Concept: Cost-Effectiveness^[e]

With Assessment	Output: Gear Ratios	Innovation Elasticity[f] Δ Output : Δ Input	Input: Main Components
			Total	Gearsets	Brakes	Clutches
W5A Ref. Object	${\displaystyle n_{O1}}$ ${\displaystyle n_{O2}}$	Topic[f]	${\displaystyle n_{I}=n_{G}+}$ ${\displaystyle n_{B}+n_{C}}$	${\displaystyle n_{G1}}$ ${\displaystyle n_{G2}}$	${\displaystyle n_{B1}}$ ${\displaystyle n_{B2}}$	${\displaystyle n_{C1}}$ ${\displaystyle n_{C2}}$
Δ Number	${\displaystyle n_{O1}-n_{O2}}$		${\displaystyle n_{I1}-n_{I2}}$	${\displaystyle n_{G1}-n_{G2}}$	${\displaystyle n_{B1}-n_{B2}}$	${\displaystyle n_{C1}-n_{C2}}$
Relative Δ	Δ Output ${\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}}$	${\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}:{\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}$ ${\displaystyle ={\tfrac {n_{O1}-n_{O2}}{n_{O2}}}\cdot {\tfrac {n_{I2}}{n_{I1}-n_{I2}}}}$	Δ Input ${\displaystyle {\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}$	${\displaystyle {\tfrac {n_{G1}-n_{G2}}{n_{G2}}}}$	${\displaystyle {\tfrac {n_{B1}-n_{B2}}{n_{B2}}}}$	${\displaystyle {\tfrac {n_{C1}-n_{C2}}{n_{C2}}}}$
W5A W4A[g]	5[h] 4[h]	Progress[f]	11 8	4[i] 3[i]	4 3	3 2
Δ Number	1		3	1	1	1
Relative Δ	0.250 ${\displaystyle {\tfrac {1}{4}}}$	0.667[f] ${\displaystyle {\tfrac {1}{4}}:{\tfrac {3}{8}}={\tfrac {1}{4}}\cdot {\tfrac {8}{3}}={\tfrac {2}{3}}}$	0.375 ${\displaystyle {\tfrac {3}{8}}}$	0.333 ${\displaystyle {\tfrac {1}{3}}}$	0.333 ${\displaystyle {\tfrac {1}{3}}}$	0.500 ${\displaystyle {\tfrac {1}{2}}}$
W5A ZF 5HP 18	5[h] 5[h]	Early Market Position[f]	11 10	4[i] 3[i]	4 3	3 4
Δ Number	0		1	1	1	-1
Relative Δ	0.000 ${\displaystyle {\tfrac {0}{5}}}$	0.000[f] ${\displaystyle {\tfrac {0}{5}}:{\tfrac {1}{10}}={\tfrac {0}{5}}\cdot {\tfrac {10}{1}}={\tfrac {0}{1}}}$	0.100 ${\displaystyle {\tfrac {1}{10}}}$	0.333 ${\displaystyle {\tfrac {1}{3}}}$	1.000 ${\displaystyle {\tfrac {2}{2}}}$	−0.250 ${\displaystyle {\tfrac {-1}{4}}}$
W5A ZF 5HP 30	5[h] 5[h]	Late Market Position[f]	11 9	4[i] 3	4 3	3 3
Δ Number	0		2	1	1	0
Relative Δ	0.000 ${\displaystyle {\tfrac {0}{5}}}$	0.000[f] ${\displaystyle {\tfrac {0}{5}}:{\tfrac {2}{9}}={\tfrac {0}{5}}\cdot {\tfrac {9}{2}}={\tfrac {0}{1}}}$	0.222 ${\displaystyle {\tfrac {2}{9}}}$	0.333 ${\displaystyle {\tfrac {1}{3}}}$	0.333 ${\displaystyle {\tfrac {1}{3}}}$	0.000 ${\displaystyle {\tfrac {0}{4}}}$
W5A 3-Speed[j]	5[h] 3[h]	Historical Market Position[f]	11 7	4[i] 2	4 3	3 2
Δ Number	2		4	2	1	1
Relative Δ	0.667 ${\displaystyle {\tfrac {2}{3}}}$	1.167[f] ${\displaystyle {\tfrac {2}{3}}:{\tfrac {4}{7}}={\tfrac {2}{3}}\cdot {\tfrac {7}{4}}={\tfrac {7}{6}}}$	0.571 ${\displaystyle {\tfrac {4}{7}}}$	1.000 ${\displaystyle {\tfrac {2}{2}}}$	0.333 ${\displaystyle {\tfrac {1}{3}}}$	0.500 ${\displaystyle {\tfrac {1}{2}}}$
[a] regular bousing for gear 1 to 4 and reverse gear · supplemental housing for gear 5 [b] hydraulic for gear 1 to 4 and reverse gear · electronic for gear 5 [c] 3 simple planetary gearsets, 3 brakes, 3 clutches [d] electronic [e] Progress increases cost-effectiveness and is reflected in the ratio of forward gears to main components. It depends on the power flow: parallel: using the two degrees of freedom of planetary gearsets to increase the number of gears with unchanged number of components serial: in-line combined planetary gearsets without using the two degrees of freedom to increase the number of gears a corresponding increase in the number of components is unavoidable [f] Innovation Elasticity Classifies Progress And Market Position Automobile manufacturers drive forward technical developments primarily in order to remain competitive or to achieve or defend technological leadership. This technical progress has therefore always been subject to economic constraints Only innovations whose relative additional benefit is greater than the relative additional resource input, i.e. whose economic elasticity is greater than 1, are considered for realization The required innovation elasticity of an automobile manufacturer depends on its expected return on investment. The basic assumption that the relative additional benefit must be at least twice as high as the relative additional resource input helps with orientation negative, if the output increases and the input decreases, is perfect 2 or above is good 1 or above is acceptable (red) below this is unsatisfactory (bold) [g] Direct Predecessor To reflect the progress of the specific model change [h] plus 1 reverse gear [i] of which 2 gearsets are combined as a compound Ravigneaux gearset [j] Historical Reference Standard (Benchmark) 3-speed transmissions with torque converters have established the modern market for automatic transmissions and thus made it possible in the first place, as this design proved to be a particularly successful compromise between cost and performance It became the archetype and dominated the world market for around 3 decades, setting the standard for automatic transmissions. It was only when fuel consumption became the focus of interest that this design reached its limits, which is why it has now completely disappeared from the market What has remained is the orientation that it offers as a reference standard (point of reference, benchmark) for this market for determining progressiveness and thus the market position of all other, later designs All transmission variants consist of 7 main components Typical examples are Turbo-Hydramatic from GM Cruise-O-Matic from Ford TorqueFlite from Chrysler Detroit Gear from BorgWarner for Studebaker BW-35 from BorgWarner and as T35 from Aisin 3N 71 from Nissan/Jatco 3 HP from ZF Friedrichshafen W3A 040 and W3B 050 from Mercedes-Benz

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Gearset Concept: Quality

The most obvious flaw of the gearset concept is the second gear, which is clearly too short, but this affected all Mercedes-Benz transmissions, especially automatic transmissions. "The manual transmission plays a key role in the positive impression made by the small V8 engine in the large S-Class sedan. It simply suits the sporty performance characteristics of the engine better than the automatic transmission, although there is still room for improvement in terms of gear ratios. 2nd gear in particular seems a little too short with a range of only 90 km/h."^[B]

After Hans-Joachim Foerster, the originator of this flawed gear ratio, left the company in November 1982,^[3] Mercedes-Benz began to address this problem. This led to the introduction of the W4A 040 II with modified gear ratios in 1985. With the 7G-Tronic transmission from 2003, they finally succeeded in completely resolving this issue.

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Gear Ratio Analysis^[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		Simple				Avg.[i]
Model Type	Version First Delivery	S1[j] R1[k]	S2[l] R2[m]	S3[n] R3[o]	S4[p] R4[q]	Brakes Clutches	Ratio Span	Gear Step[r]
Gear		R		1	2	3	4	5
Gear Ratio[b]		${\displaystyle {i_{R}}}$[b]		${\displaystyle {i_{1}}}$[b]	${\displaystyle {i_{2}}}$[b]	${\displaystyle {i_{3}}}$[b]	${\displaystyle {i_{4}}}$[b]	${\displaystyle {i_{5}}}$[b]
Step[r]		${\displaystyle -{\frac {i_{R}}{i_{1}}}}$[s]		${\displaystyle {\frac {i_{1}}{i_{1}}}}$	${\displaystyle {\frac {i_{1}}{i_{2}}}}$[t]	${\displaystyle {\frac {i_{2}}{i_{3}}}}$	${\displaystyle {\frac {i_{3}}{i_{4}}}}$	${\displaystyle {\frac {i_{4}}{i_{5}}}}$
Δ Step[u][v]					${\displaystyle {\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}}$	${\displaystyle {\tfrac {i_{2}}{i_{3}}}:{\tfrac {i_{3}}{i_{4}}}}$	${\displaystyle {\tfrac {i_{3}}{i_{4}}}:{\tfrac {i_{4}}{i_{5}}}}$
Shaft Speed		${\displaystyle {\frac {i_{1}}{i_{R}}}}$		${\displaystyle {\frac {i_{1}}{i_{1}}}}$	${\displaystyle {\frac {i_{1}}{i_{2}}}}$	${\displaystyle {\frac {i_{1}}{i_{3}}}}$	${\displaystyle {\frac {i_{1}}{i_{4}}}}$	${\displaystyle {\frac {i_{1}}{i_{5}}}}$
Δ Shaft Speed[w]		${\displaystyle 0-{\tfrac {i_{1}}{i_{R}}}}$		${\displaystyle {\tfrac {i_{1}}{i_{1}}}-0}$	${\displaystyle {\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{4}}}-{\tfrac {i_{1}}{i_{3}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{5}}}-{\tfrac {i_{1}}{i_{4}}}}$
Torque Ratio[c]		${\displaystyle \mu _{R}}$[c]		${\displaystyle \mu _{1}}$[c]	${\displaystyle \mu _{2}}$[c]	${\displaystyle \mu _{3}}$[c]	${\displaystyle \mu _{4}}$[c]	${\displaystyle \mu _{5}}$[c]
Efficiency ${\displaystyle \eta _{n}}$[d]		${\displaystyle {\frac {\mu _{R}}{i_{R}}}}$[d]		${\displaystyle {\frac {\mu _{1}}{i_{1}}}}$[d]	${\displaystyle {\frac {\mu _{2}}{i_{2}}}}$[d]	${\displaystyle {\frac {\mu _{3}}{i_{3}}}}$[d]	${\displaystyle {\frac {\mu _{4}}{i_{4}}}}$[d]	${\displaystyle {\frac {\mu _{5}}{i_{5}}}}$[d]
W4A 040 I 722.3	40 kp⋅m (392 N⋅m; 289 lb⋅ft) 1979[C][4]	34 50	50 78	34 78		3 2	3.6759 3.6759	1.9173
								1.5433[r]
Gear		R		1	2	3	4	5
Gear Ratio[b]		−5.1388[s] ${\displaystyle -{\tfrac {2,184}{425}}}$		3.6759 ${\displaystyle {\tfrac {3,584}{975}}}$	2.4123 [r][v] ${\displaystyle {\tfrac {784}{325}}}$	1.4359[r] ${\displaystyle {\tfrac {56}{39}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$
Step		1.3980[s]		1.0000	1.5238[r]	1.6800[r]	1.4359
Δ Step[u]					0.9070[v]	1.1700
Speed		-0.7153		1.0000	1.5238	2.5600	3.6759
Δ Speed		0.7153		1.0000	0.5238	1.0362	1.1159
Torque Ratio[c]		–4.9659 –4.8805		3.6091 3.5758	2.3687 2.3471	1.4272 1.4228	1.0000
Efficiency ${\displaystyle \eta _{n}}$[d]		0.9664 0.9497		0.9818 0.9728	0.9819 0.9730	0.9939 0.9909	1.0000
W4A 020 722.4	20 kp⋅m (196 N⋅m; 145 lb⋅ft) 1982[C][4]	26 42	42 78	38 78		3 2	4.2491 4.2491	2.0613
								1.6197[r]
Gear		R		1	2	3	4	5
Gear Ratio[b]		−5.6692[s] ${\displaystyle -{\tfrac {754}{133}}}$		4.2491 ${\displaystyle {\tfrac {1,160}{273}}}$	2.4078[t] ${\displaystyle {\tfrac {1,972}{819}}}$	1.4872 ${\displaystyle {\tfrac {58}{39}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$
Step		1.3342[s]		1.0000	1.7647[t]	1.6190	1.4872
Δ Step[u]					1.0900	1.0887
Speed		-0.7153		1.0000	1.7647	2.8571	4.2491
Δ Speed		0.7153		1.0000	0.7647	1.0924	1.3919
Torque Ratio[c]		–5.4811 –5.3882		4.1664 4.1253	2.3647 2.3434	1.4774 1.4726	1.0000
Efficiency ${\displaystyle \eta _{n}}$[d]		0.9668 0.9504		0.9805 0.9709	0.9821 0.9733	0.9934 0.9902	1.0000
W4A 040 II 722.3	40 kp⋅m (392 N⋅m; 289 lb⋅ft) 1985[C][4]	26 46	46 78	34 78		3 2	3.8707 3.8707	1.9674
								1.5701[r]
Gear		R		1	2	3	4	5
Gear Ratio[b]		−5.5857[s]		3.8707	2.2475[t]	1.4359	1.0000
W4A 028 722.3[x]	28 kp⋅m (275 N⋅m; 203 lb⋅ft) 1990[C][4]	26 46	46 78	34 78		3 2	3.8707	1.9674
								1.5701[r]
Gear		R		1	2	3	4	5
Gear Ratio[b]		−5.5857[s]		3.8707	2.2475[t]	1.4359	1.0000
W5A 030 722.5	30 kp⋅m (294 N⋅m; 217 lb⋅ft) 1990[C]	26 46	46 78	34 78	26 78	4 3	5.1609 5.1609	1.7038
								1.5072[r]
Gear		R		1	2	3	4	5
Gear Ratio[b]		−5.5857[s] ${\displaystyle -{\tfrac {2,184}{391}}}$		3.8707 ${\displaystyle {\tfrac {3,472}{897}}}$	2.2475[t] ${\displaystyle {\tfrac {672}{299}}}$	1.4359 ${\displaystyle {\tfrac {56}{39}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.7500 ${\displaystyle {\tfrac {3}{4}}}$
Step		1.4431[s]		1.0000	1.7222[t]	1.5652	1.4359	1.3333
Δ Step[u]					1.1003	1.0901	1.0769
Speed		-0.6930		1.0000	1.7222	2.6957	3.8707	5.1609
Δ Speed		0.6930		1.0000	0.7222	0.9734	1.1750	1.2902
Torque Ratio[c]		–5.3977 –5.3049		3.7988 3.7631	2.2098 2.1911	1.4272 1.4228	1.0000	0.7462 0.7442
Efficiency ${\displaystyle \eta _{n}}$[d]		0.9664 0.9497		0.9814 0.9722	0.9832 0.9749	0.9939 0.9909	1.0000	0.9949 0.9923
Actuated Shift Elements
Brake A[y]					❶
Brake B[z]				❶	❶	❶
Brake R[aa]		❶
Brake S[ab]								❶[ac]
Clutch E[ad]						❶	❶	❶
Clutch F[ae]		❶		❶			❶	❶
Clutch S[af]		❶[ac]		❶[ac]	❶[ac]	❶[ac]	❶[ac]
Geometric Ratios: Speed Conversion
Gear Ratio[b] R & 3 Ordinary[ag] Elementary Noted[ah]	${\displaystyle {i_{R}}=-{\frac {R_{2}(S_{3}+R_{3})}{S_{2}S_{3}}}}$					${\displaystyle {i_{3}}={\frac {S_{3}+R_{3}}{R_{3}}}}$
	${\displaystyle {i_{R}}=-{\tfrac {R_{2}}{S_{2}}}\left(1+{\tfrac {R_{3}}{S_{3}}}\right)}$					${\displaystyle {i_{3}}=1+{\tfrac {S_{3}}{R_{3}}}}$
Gear Ratio[b] 1 & 4 Ordinary[ag] Elementary Noted[ah]	${\displaystyle {i_{1}}={\frac {(S_{2}+R_{2})(S_{3}+R_{3})}{S_{2}R_{3}}}}$					${\displaystyle {i_{4}}={\frac {1}{1}}}$
	${\displaystyle {i_{1}}=\left(1+{\tfrac {R_{2}}{S_{2}}}\right)\left(1+{\tfrac {S_{3}}{R_{3}}}\right)}$
Gear Ratio[b] 2 & 5[ac] Ordinary[ag] Elementary Noted[ah]	${\displaystyle {i_{2}}={\frac {(S_{1}+R_{1})(S_{3}+R_{3})}{R_{1}R_{3}}}}$					${\displaystyle {i_{5}}={\frac {R_{4}}{S_{4}+R_{4}}}}$[ac]
	${\displaystyle {i_{2}}=\left(1+{\tfrac {S_{1}}{R_{1}}}\right)\left(1+{\tfrac {S_{3}}{R_{3}}}\right)}$					${\displaystyle {i_{5}}={\tfrac {1}{1+{\tfrac {S_{4}}{R_{4}}}}}}$[ac]
Kinetic Ratios: Torque Conversion
Specific Torque[d] R & 3	${\displaystyle \mu _{R}=-{\tfrac {R_{2}}{S_{2}}}\eta _{0}\left(1+{\tfrac {R_{3}}{S_{3}}}\eta _{0}\right)}$					${\displaystyle \mu _{3}=1+{\tfrac {S_{3}}{R_{3}}}\eta _{0}}$
Specific Torque[d] 1 & 4	${\displaystyle \mu _{1}=\left(1+{\tfrac {R_{2}}{S_{2}}}\eta _{0}\right)\left(1+{\tfrac {S_{3}}{R_{3}}}\eta _{0}\right)}$					${\displaystyle \mu _{4}={\tfrac {1}{1}}}$
Specific Torque[d] 2 & 5[ac]	${\displaystyle \mu _{2}=\left(1+{\tfrac {S_{1}}{R_{1}}}{\eta _{0}}^{\tfrac {3}{2}}\right)\left(1+{\tfrac {S_{3}}{R_{3}}}\eta _{0}\right)}$					${\displaystyle \mu _{5}={\tfrac {1}{1+{\tfrac {S_{4}}{R_{4}}}\cdot {\tfrac {1}{\eta _{0}}}}}}$[ac]
[a] Revised 14 January 2026 Nomenclature ${\displaystyle S_{n}=}$ sun gear: number of teeth ${\displaystyle R_{n}=}$ ring gear: number of teeth ${\displaystyle \color {gray}{C_{n}=}}$ carrier or planetary gear carrier (not needed) ${\displaystyle s_{n}=}$ sun gear: shaft speed ${\displaystyle r_{n}=}$ ring gear: shaft speed ${\displaystyle c_{n}=}$ carrier or planetary gear carrier: shaft speed With ${\displaystyle n=}$ gear is ${\displaystyle i_{n}=}$ gear ratio or transmission ratio ${\displaystyle \omega _{1;n}=\omega _{t}=}$ shaft speed shaft 1: input (turbine) shaft ${\displaystyle \omega _{2;n}=}$ shaft speed shaft 2: output shaft ${\displaystyle T_{1;n}=T_{t}=}$ torque shaft 1: input (turbine) shaft ${\displaystyle T_{2;n}=}$ torque shaft 2: output shaft ${\displaystyle \mu _{n}=}$ torque ratio or torque conversion ratio ${\displaystyle \eta _{n}=}$ efficiency ${\displaystyle i_{0}=}$ stationary gear ratio ${\displaystyle \eta _{0}=}$ (assumed) stationary gear efficiency [b] Gear Ratio (Transmission Ratio) ${\displaystyle i_{n}}$ — Speed Conversion — The gear ratio ${\displaystyle i_{n}}$ is the ratio of input shaft speed ${\displaystyle \omega _{1;n}}$ to output shaft speed ${\displaystyle \omega _{2;n}}$ and therefore corresponds to the reciprocal of the shaft speeds ${\displaystyle i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}}$ [c] Torque Ratio (Torque Conversion Ratio) ${\displaystyle \mu _{n}}$ — Torque Conversion — The torque ratio ${\displaystyle \mu _{n}}$ is the ratio of output torque ${\displaystyle T_{2;n}}$ to input torque ${\displaystyle T_{1;n}}$ minus efficiency losses and therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too ${\displaystyle \mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}}$ whereby ${\displaystyle \eta _{n;\eta _{0}}}$ may vary from gear to gear according to the formulas listed in this table and ${\displaystyle 0\leq \eta _{n;\eta _{0}}\leq 1}$ [d] Efficiency The efficiency ${\displaystyle \eta _{n}}$ is calculated from the torque ratio in relation to the gear ratio (transmission ratio) ${\displaystyle \eta _{n}={\frac {\mu _{n}}{i_{n}}}}$ 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 ${\displaystyle i_{0}}$ 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 ${\displaystyle \eta _{0}}$ specified here are based on assumed efficiencies for the stationary ratio ${\displaystyle i_{0}}$ of ${\displaystyle \eta _{0}=0.9800}$ (upper value) and ${\displaystyle \eta _{0}=0.9700}$ (lower value) for both interventions together The corresponding efficiency for single-meshing gear pairs is ${\displaystyle {\eta _{0}}^{\tfrac {1}{2}}}$ at ${\displaystyle 0.9800^{\tfrac {1}{2}}=0.98995}$ (upper value) and ${\displaystyle 0.9700^{\tfrac {1}{2}}=0.98489}$ (lower value) [e] Layout Input and output are on opposite sides Planetary gearset 1 (the inner Ravigneaux gearset) is on the input (turbine) side Input (turbine) shafts is S2 Output shaft is C3 Output shaft W5A 030 is R4 [f] Total Ratio Span (Total Gear/Transmission Ratio) Nominal ${\displaystyle {\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}}$ 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 [g] Total Ratio Span (Total Gear Ratio/Total Transmission Ratio) Effective ${\displaystyle {\frac {\omega _{2;n}}{max(\omega _{2;1};|\omega _{2;R}|)}}={\frac {min(i_{1};|i_{R}|)}{i_{n}}}}$ 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 [h] Ratio Span's Center ${\displaystyle (i_{1}i_{n})^{\frac {1}{2}}}$ The center indicates the speed level of the transmission Together with the final drive ratio it gives the shaft speed level of the vehicle [i] Average Gear Step ${\displaystyle \left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}}$ There are ${\displaystyle n-1}$ gear steps between ${\displaystyle n}$ gears with decreasing step width the gears connect better to each other shifting comfort increases [j] Sun 1: sun gear of gearset 1: inner Ravigneaux gearset [k] Ring 1: ring gear of gearset 1: inner Ravigneaux gearset [l] Sun 2: sun gear of gearset 2: outer Ravigneaux gearset [m] Ring 2: ring gear of gearset 2: outer Ravigneaux gearset [n] Sun 3: sun gear of gearset 3 [o] Ring 3: ring gear of gearset 3 [p] Sun 4: sun gear of gearset 4 · W5A 030 only [q] Ring 4: ring gear of gearset 4 · W5A 030 only [r] 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 · W5A 030: the first 2) is always larger and the upper half of the gear steps (between the large gears; rounded up, here the last 2) 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) [s] 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/Transmission Ratio) Effective [t] 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) [u] From large to small gears (from right to left) [v] 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) [w] 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) [x] W4A 028: for off-road applications (RWD and 4X4) [y] Blocks S1 (sun gear of the inner Ravigneaux gearset) [z] Blocks S3 [aa] Blocks C1/C2 (the common carrier of the compound Ravigneaux gearset) [ab] Blocks S4 (Overdrive: German: S for "schnell", fast) · W5A 030 only [ac] W5A 030 only [ad] Couples S1 (the sun gear of the inner Ravigneaux gearset) with C1/C2 (the common carrier of the compound Ravigneaux gearset) [ae] Couples R2 and S3 [af] Couples S4 with R4 (Overdrive: German: S for "schnell", fast) · W5A 030 only [ag] Ordinary Noted For direct determination of the gear ratio [ah] 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 ratio and efficiency

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