TheFord–GM 10-speed automatic transmission is part of a joint venture betweenFord Motor Company andGeneral Motors to design and engineer two transmissions: alongitudinal 10-speed transmission and atransverse 9-speed trans-axle. Each company manufactures its own unique version of the transmissions in its own factories.^[1][2] The 10-speed transmission was designed by Ford, while the 9-speed transmission was designed by GM.^[3][4]

The10R 80 was first produced at the Ford Livonia Transmission Plant inLivonia, Michigan, and the Hydra-Matic10L 80 is made at the General Motors Romulus Powertrain Plant, inRomulus, Michigan.^[5] GM's Silao, Mexico, transmission plant started10L 80 production in 2018,^[6] while Ford'sSharonville Transmission plant started10R 80 production in 2018.^[7]

Gearset Concept: Cost-Effectiveness^[a]

With Assessment	Output: Gear Ratios	Innovation Elasticity[b] Δ Output : Δ Input	Input: Main Components
			Total	Gearsets	Brakes	Clutches
10R & 10L 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 ${\displaystyle \frac{n_{O1}-n_{O2}}{n_{O2}}}$	${\displaystyle \frac{n_{O1}-n_{O2}}{n_{O2}}:\frac{n_{I1}-n_{I2}}{n_{I2}}}$ ${\displaystyle =\frac{n_{O1}-n_{O2}}{n_{O2}}\cdot \frac{n_{I2}}{n_{I1}-n_{I2}}}$	Δ Input ${\displaystyle \frac{n_{I1}-n_{I2}}{n_{I2}}}$	${\displaystyle \frac{n_{G1}-n_{G2}}{n_{G2}}}$	${\displaystyle \frac{n_{B1}-n_{B2}}{n_{B2}}}$	${\displaystyle \frac{n_{C1}-n_{C2}}{n_{C2}}}$
GM 10L GM 8L[c]	10[d] 8[d]	Progress General Motors[b]	10 9	4 4	2 2	4 3
Δ Number	2		1	0	0	1
Relative Δ	0.250 ${\displaystyle \frac{2}{8}}$	2.250[b] ${\displaystyle \frac{2}{8}:\frac{1}{9}=\frac{1}{4}\cdot \frac{9}{1}=\frac{9}{4}}$	0.111 ${\displaystyle \frac{1}{9}}$	0.000 ${\displaystyle \frac{0}{4}}$	0.000 ${\displaystyle \frac{0}{2}}$	0.333 ${\displaystyle \frac{1}{3}}$
Ford 10R Ford 6R[c]	10[d] 6[d]	Progress Ford[b]	10 8	4 3	2 2	4 3
Δ Number	4		2	1	0	1
Relative Δ	0.667 ${\displaystyle \frac{4}{6}}$	2.667[b] ${\displaystyle \frac{4}{6}:\frac{2}{8}=\frac{2}{3}\cdot \frac{4}{1}=\frac{8}{3}}$	0.250 ${\displaystyle \frac{2}{8}}$	0.333 ${\displaystyle \frac{1}{3}}$	0.000 ${\displaystyle \frac{0}{2}}$	0.333 ${\displaystyle \frac{1}{3}}$
10R & 10L 8HP[e]	10[d] 8[d]	Current Market Position[b]	10 8	4 4	2 2	4 3
Δ Number	2		1	0	0	1
Relative Δ	0.250 ${\displaystyle \frac{2}{8}}$	2.250[b] ${\displaystyle \frac{2}{8}:\frac{1}{9}=\frac{1}{4}\cdot \frac{9}{1}=\frac{9}{4}}$	0.111 ${\displaystyle \frac{1}{9}}$	0.000 ${\displaystyle \frac{0}{4}}$	0.000 ${\displaystyle \frac{0}{2}}$	0.333 ${\displaystyle \frac{1}{3}}$
10R & 10L 3-Speed[f]	10[d] 3[d]	Historical Market Position[b]	10 7	4 2	2 3	4 2
Δ Number	7		3	2	-1	2
Relative Δ	2.333 ${\displaystyle \frac{7}{3}}$	5.444[b] ${\displaystyle \frac{7}{3}:\frac{3}{7}=\frac{7}{3}\cdot \frac{7}{3}=\frac{49}{9}}$	0.429 ${\displaystyle \frac{3}{7}}$	1.000 ${\displaystyle \frac{2}{2}}$	−0.333 ${\displaystyle \frac{-1}{3}}$	1.000 ${\displaystyle \frac{2}{2}}$
^Progress increases cost-effectiveness and is reflected in theratio of forward gears to main components. It depends on thepower flow: parallel: using the two degrees of freedom ofplanetary gearsets to increase the number of gears with unchanged number of components serial: in-line combinedplanetary gearsets without using the two degrees of freedom to increase the number of gears a corresponding increase in the number of components is unavoidable ^abcdefghijInnovationElasticity 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. whoseeconomicelasticity is greater than 1, are considered for realization Therequired innovationelasticity of an automobile manufacturer depends on its expected return on investment. The basic assumption that the relative additional benefit must beat 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) ^abDirect Predecessor To reflect the progress of the specific model change ^abcdefghplus 1 reverse gear ^Current Reference Standard (Benchmark) The 8HP has become the new reference standard (benchmark) for automatic transmissions ^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 fromGM Cruise-O-Matic fromFord TorqueFlite fromChrysler Detroit Gear fromBorgWarner forStudebaker BW-35 fromBorgWarner and asT35 fromAisin 3N 71 fromNissan/Jatco 3 HP fromZF Friedrichshafen W3A 040 and W3B 050 fromMercedes-Benz

The transmission is based on the well-known 8-speed automatic transmission8HP fromZF. A unique triple-clutch assembly on a dedicated intermediate shaft, placed in the middle of the architecture, replaces two ordinary clutches and is the key for packaging the 10-speed unit into the same space as the previous transmission.^[8]

• Compared to the 8-speed architecture
  • The transmission offers smaller steps between the lower gears
  • Which benefits acceleration at low speeds.
  • The transmission does not offer any significantly smaller steps between the upper gears
  • Where this is more important than in the lower gears.
  • The transmission does not offer any increase in the overall range.
• The ratios of the 10 gears are
  • much more unevenly distributed than in the 8-speed architecture
  • and even more uneven than in the direct competitor9G-Tronic fromMercedes-Benz.
  • The gear step from 9th to 10th gear is unfavorably small at less than 9%.

These weaknesses largely offset the advantage of the additional gears.

Gear Ratio Analysis

In-Depth Analysis With Assessment[a]					Planetary Gearset: Teeth[b]				Count	Nomi- nal[c] Effec- tive[d]	Center[e]
											Avg.[f]
Model Type	Version First Delivery				S1[g] R1[h]	S2[i] R2[j]	S3[k] R3[l]	S4[m] R4[n]	Brakes Clutches	Ratio Span	Gear Step[o]
Gear Ratio	R ${\displaystyle i_R}$	1 ${\displaystyle i_1}$	2 ${\displaystyle i_2}$	3 ${\displaystyle i_3}$	4 ${\displaystyle i_4}$	5 ${\displaystyle i_5}$	6 ${\displaystyle i_6}$	7 ${\displaystyle i_7}$	8 ${\displaystyle i_8}$	9 ${\displaystyle i_9}$	10 ${\displaystyle i_{10}}$
Step[o]	${\displaystyle -\frac{i_R}{i_1}}$[p]	${\displaystyle \frac{i_1}{i_1}}$	${\displaystyle \frac{i_1}{i_2}}$[q]	${\displaystyle \frac{i_2}{i_3}}$	${\displaystyle \frac{i_3}{i_4}}$	${\displaystyle \frac{i_4}{i_5}}$	${\displaystyle \frac{i_5}{i_6}}$	${\displaystyle \frac{i_6}{i_7}}$	${\displaystyle \frac{i_7}{i_8}}$	${\displaystyle \frac{i_8}{i_9}}$	${\displaystyle \frac{i_9}{i_{10}}}$
Δ Step[r][s]			${\displaystyle \frac{i_1}{i_2}:\frac{i_2}{i_3}}$	${\displaystyle \frac{i_2}{i_3}:\frac{i_3}{i_4}}$	${\displaystyle \frac{i_3}{i_4}:\frac{i_4}{i_5}}$	${\displaystyle \frac{i_4}{i_5}:\frac{i_5}{i_6}}$	${\displaystyle \frac{i_5}{i_6}:\frac{i_6}{i_7}}$	${\displaystyle \frac{i_6}{i_7}:\frac{i_7}{i_8}}$	${\displaystyle \frac{i_7}{i_8}:\frac{i_8}{i_9}}$	${\displaystyle \frac{i_8}{i_9}:\frac{i_9}{i_{10}}}$
Shaft Speed	${\displaystyle \frac{i_1}{i_R}}$	${\displaystyle \frac{i_1}{i_1}}$	${\displaystyle \frac{i_1}{i_2}}$	${\displaystyle \frac{i_1}{i_3}}$	${\displaystyle \frac{i_1}{i_4}}$	${\displaystyle \frac{i_1}{i_5}}$	${\displaystyle \frac{i_1}{i_6}}$	${\displaystyle \frac{i_1}{i_7}}$	${\displaystyle \frac{i_1}{i_8}}$	${\displaystyle \frac{i_1}{i_9}}$	${\displaystyle \frac{i_1}{i_{10}}}$
Δ Shaft Speed[t]	${\displaystyle 0-\frac{i_1}{i_R}}$	${\displaystyle \frac{i_1}{i_1}-0}$	${\displaystyle \frac{i_1}{i_2}-\frac{i_1}{i_1}}$	${\displaystyle \frac{i_1}{i_3}-\frac{i_1}{i_2}}$	${\displaystyle \frac{i_1}{i_4}-\frac{i_1}{i_3}}$	${\displaystyle \frac{i_1}{i_5}-\frac{i_1}{i_4}}$	${\displaystyle \frac{i_1}{i_6}-\frac{i_1}{i_5}}$	${\displaystyle \frac{i_1}{i_7}-\frac{i_1}{i_6}}$	${\displaystyle \frac{i_1}{i_8}-\frac{i_1}{i_7}}$	${\displaystyle \frac{i_1}{i_9}-\frac{i_1}{i_8}}$	${\displaystyle \frac{i_1}{i_{10}}-\frac{i_1}{i_9}}$
Specific Torque[u]	${\displaystyle \frac{T_{2;R}}{T_{1;R}}}$[v]	${\displaystyle \frac{T_{2;1}}{T_{1;1}}}$[v]	${\displaystyle \frac{T_{2;2}}{T_{1;2}}}$[v]	${\displaystyle \frac{T_{2;3}}{T_{1;3}}}$[v]	${\displaystyle \frac{T_{2;4}}{T_{1;4}}}$[v]	${\displaystyle \frac{T_{2;5}}{T_{1;5}}}$[v]	${\displaystyle \frac{T_{2;6}}{T_{1;6}}}$[v]	${\displaystyle \frac{T_{2;7}}{T_{1;7}}}$[v]	${\displaystyle \frac{T_{2;8}}{T_{1;8}}}$[v]	${\displaystyle \frac{T_{2;9}}{T_{1;9}}}$[v]	${\displaystyle \frac{T_{2;10}}{T_{1;10}}}$[v]
Efficiency ${\displaystyle {\eta }_n}$[u]	${\displaystyle \frac{T_{2;R}}{T_{1;R}}:i_R}$	${\displaystyle \frac{T_{2;1}}{T_{1;1}}:i_1}$	${\displaystyle \frac{T_{2;2}}{T_{1;2}}:i_2}$	${\displaystyle \frac{T_{2;3}}{T_{1;3}}:i_3}$	${\displaystyle \frac{T_{2;4}}{T_{1;4}}:i_4}$	${\displaystyle \frac{T_{2;5}}{T_{1;5}}:i_5}$	${\displaystyle \frac{T_{2;6}}{T_{1;6}}:i_6}$	${\displaystyle \frac{T_{2;7}}{T_{1;7}}:i_7}$	${\displaystyle \frac{T_{2;8}}{T_{1;8}}:i_8}$	${\displaystyle \frac{T_{2;9}}{T_{1;9}}:i_9}$	${\displaystyle \frac{T_{2;10}}{T_{1;10}}:i_{10}}$
Ford 10R 80 GM 10L 80 GM 10L 90	800 N⋅m (590 lb⋅ft) · 2017[9] 900 N⋅m (664 lb⋅ft) · 2018				45 95	51 89[10]	73 119	23 85[10]	2 4	7.3864 7.3864	1.7277
											1.2488[o]
Gear Ratio	−4.8661 ${\displaystyle -\frac{40,851}{8,395}}$	4.6957 ${\displaystyle \frac{108}{23}}$	2.9851[s] ${\displaystyle \frac{2403}{805}}$	2.1462 ${\displaystyle \frac{3,024}{1,409}}$	1.7690[o][t] ${\displaystyle \frac{743}{420}}$	1.5201[o][s][t] ${\displaystyle \frac{80,244}{52,789}}$	1.2751[o][s] ${\displaystyle \frac{9,289,296}{7,285,081}}$	1.0000[o] ${\displaystyle \frac{1}{1}}$	0.8536[s][t] ${\displaystyle \frac{650,168}{720,653}}$	0.6892 ${\displaystyle \frac{3,204}{4,649}}$	0.6357[t] ${\displaystyle \frac{89}{140}}$
Step	1.0363	1.0000	1.5730	1.3909	1.2132[o]	1.1638[o]	1.1921[o]	1.2751[o]	1.1715	1.2386	1.0841
Δ Step[r]			1.1310[s]	1.1465	1.0425	0.9762[s]	0.9349[s]	1.0885	0.9458[s]	1.1425
Speed	–0.9650	1.0000	1.5730	2.1879	2.6543	3.0890	3.6825	4.6956	5.5008	6.8134	7.3864
Δ Speed	0.9650	1.0000	0.5730	0.6148	0.4665[t]	0.4347[t]	0.5935	1.0131	0.8052[t]	1.3126	0.5730[t]
Specific Torque[u]	–4.6591 –4.5573	4.6217 4.5848	2.9164 2.8821	2.1201 2.1071	1.7440 1.7316	1.5054 1.4980	1.2624 1.2559	1.0000	0.8489 0.8465	0.6839 0.6812	0.6310 0.6286
Efficiency ${\displaystyle {\eta }_n}$[u]	0.9575 0.9365	0.9843 0.9764	0.9770 0.9655	0.9879 0.9818	0.9858 0.9788	0.9903 0.9855	0.9900 0.9850	1.0000	0.9945 0.9917	0.9924 0.9885	0.9926 0.9889
Ford 10R 140	1,400 N⋅m (1,033 lb⋅ft) · 2020[11]				58 122	50 86	69 111	26 94	2 4	7.2987 7.2987	1.7084
											1.2471[o]
Gear Ratio	−4.6951 ${\displaystyle -\frac{23,865}{5,083}}$	4.6154 ${\displaystyle \frac{60}{13}}$	2.9186 ${\displaystyle \frac{645}{221}}$	2.1319 ${\displaystyle \frac{5,400}{2,533}}$	1.7733[o][t] ${\displaystyle \frac{3,497}{1,972}}$	1.5188[o][s][t] ${\displaystyle \frac{41,964}{27,629}}$	1.2773[o][s] ${\displaystyle \frac{303,768}{237,827}}$	1.0000[o] ${\displaystyle \frac{1}{1}}$	0.8514[s][t] ${\displaystyle \frac{6,192}{7,273}}$	0.6871 ${\displaystyle \frac{516}{751}}$	0.6324[t] ${\displaystyle \frac{43}{68}}$
Step	1.0173	1.0000	1.5814	1.3690	1.2022[o]	1.1676[o]	1.1891[o]	1.2773[o]	1.1746	1.2391	1.0866
Δ Step[r]			1.1551	1.1388	1.0297	0.9819[s]	0.9310[s]	1.0874	0.9479[s]	1.1404
Speed	–0.9830	1.0000	1.5814	2.1650	2.6027	3.0388	3.6135	4.6154	5.4211	6.7174	7.2987
Δ Speed	0.9830	1.0000	0.5814	0.5836	0.4377[t]	0.4360[t]	0.5747	1.0019	0.8058[t]	1.2962	0.5814[t]
Specific Torque[u]	–4.4953 –4.3972	4.5431 4.5069	2.8514 2.8179	2.1061 2.0931	1.7482 1.7357	1.5041 1.4967	1.2644 1.2579	1.0000	0.8466 0.8442	0.6818 0.6791	0.6276 0.6252
Efficiency ${\displaystyle {\eta }_n}$[u]	0.9575 0.9366	0.9843 0.9765	0.9770 0.9655	0.9879 0.9818	0.9858 0.9788	0.9903 0.9854	0.9899 0.9848	1.0000	0.9944 0.9916	0.9923 0.9883	0.9926 0.9888
GM 10L 1000 (Allison)	1,400 N⋅m (1,033 lb⋅ft) · 2020[12]				53 103	53 91	65 103	26 92	2 4	7.1817 7.1817	1.6935
											1.2449[o]
Gear Ratio	−4.5448 ${\displaystyle -\frac{553,007}{121,680}}$	4.5385 ${\displaystyle \frac{59}{13}}$	2.8681[s] ${\displaystyle \frac{413}{144}}$	2.0609 ${\displaystyle \frac{4,602}{2,233}}$	1.7153[o][t] ${\displaystyle \frac{247}{144}}$	1.4817[o][s][t] ${\displaystyle \frac{14,573}{9,835}}$	1.2583[o][s] ${\displaystyle \frac{57,702}{45,857}}$	1.0000[o] ${\displaystyle \frac{1}{1}}$	0.8506[s][t] ${\displaystyle \frac{34,692}{40,787}}$	0.6877 ${\displaystyle \frac{5,369}{7,807}}$	0.6319[t] ${\displaystyle \frac{91}{144}}$
Step	1.0014	1.0000	1.5824	1.3916	1.2015[o]	1.1576[o]	1.1776[o]	1.2583[o]	1.1757	1.2368	1.0883
Δ Step[r]			1.1371[s]	1.1583	1.0379	0.9830[s]	0.9358[s]	1.0703	0.9506[s]	1.1365
Speed	–0.9986	1.0000	1.5824	2.2022	2.6459	3.0629	3.6068	4.5386	5.3358	6.5993	7.1817
Δ Speed	0.9986	1.0000	0.5824	0.6198	0.4437[t]	0.4170[t]	0.5439	0.9317	0.7974[t]	1.2635	0.5824[t]
Specific Torque[u]	–4.3517 –4.2569	4.4677 4.4323	2.8023 2.7694	2.0362 2.0239	1.6920 1.6805	1.4679 1.4610	1.2459 1.2396	1.0000	0.8458 0.8434	0.6824 0.6797	0.6272 0.6248
Efficiency ${\displaystyle {\eta }_n}$[u]	0.9575 0.9366	0.9844 0.9766	0.9771 0.9656	0.9880 0.9820	0.9865 0.9797	0.9907 0.9860	0.9902 0.9852	1.0000	0.9944 0.9915	0.9923 0.9883	0.9925 0.9887
Ford 10R 60	600 N⋅m (443 lb⋅ft) · 2020[13]				45 95	51 89[10]	73 119	28 104	2 4	7.4157 7.4157	1.7312
											1.2493[o]
Gear Ratio	−4.8854 ${\displaystyle -\frac{49,929}{10,220}}$	4.7143 ${\displaystyle \frac{33}{7}}$	2.9969[s] ${\displaystyle \frac{2,937}{980}}$	2.1488 ${\displaystyle \frac{462}{215}}$	1.7690[o][t] ${\displaystyle \frac{743}{420}}$	1.5209[o][s][t] ${\displaystyle \frac{24,519}{16,121}}$	1.2755[o][s] ${\displaystyle \frac{1,419,198}{1,112,671}}$	1.0000[o] ${\displaystyle \frac{1}{1}}$	0.8535[s][t] ${\displaystyle \frac{93,984}{110,117}}$	0.6890 ${\displaystyle \frac{979}{1,421}}$	0.6357[t] ${\displaystyle \frac{89}{140}}$
Step	1.0363	1.0000	1.5730	1.3947	1.2147[o]	1.1631[o]	1.1924[o]	1.2755[o]	1.1717	1.2389	1.0837
Δ Step[r]			1.1279[s]	1.1482	1.0443	0.9754[s]	0.9349[s]	1.0886	0.9458[s]	1.1431
Speed	–0.9650	1.0000	1.5730	2.1979	2.6648	3.0996	3.6961	4.7143	5.5235	6.8143	7.4157
Δ Speed	0.9650	1.0000	0.5730	0.6208	0.4710[t]	0.4347[t]	0.5965	1.0182	0.8092[t]	1.3192	0.5730[t]
Specific Torque[u]	–4.6775 –4.5753	4.6400 4.6029	2.9279 2.8935	2.1227 2.1096	1.7440 1.7316	1.5062 1.4989	1.2627 1.2563	1.0000	0.8488 0.8464	0.6837 0.6810	0.6310 0.6286
Efficiency ${\displaystyle {\eta }_n}$[u]	0.9574 0.9365	0.9842 0.9764	0.9770 0.9655	0.9878 0.9818	0.9858 0.9788	0.9903 0.9855	0.9900 0.9850	1.0000	0.9945 0.9917	0.9924 0.9885	0.9926 0.9889
Actuated Shift Elements[w]
Brake A[x]	❶	❶	❶						❶	❶	❶
Brake B[y]	❶	❶	❶	❶	❶	❶	❶
Clutch C[z]			❶	❶	❶	❶		❶		❶	❶
Clutch D[aa]	❶	(❶)	❶	❶	❶		❶	❶	❶		❶
Clutch E[ab]		❶		❶		❶	❶	❶	❶	❶
Clutch F[ac]	❶				❶	❶	❶	❶	❶	❶	❶
Gears UsingZF 8HP Logic And New Gears
ZF 8HP	R	1	2	3	4	5		6	7		8
10R & 10L	New	1	2	3	4	New	New	7	New	New	10
Geometric Ratios
Ratio R–2 & 10 Ordinary[ad] Elementary Noted[ae]	${\displaystyle i_R=-\frac{R_2{R}_3(S_4+R_4)}{S_3{S}_4(S_2+R_2)}}$			${\displaystyle i_1=\frac{S_4+R_4}{S_4}}$		${\displaystyle i_2=\frac{R_2(S_4+R_4)}{S_4(S_2+R_2)}}$			${\displaystyle i_{10}=\frac{R_2}{S_2+R_2}}$
	${\displaystyle i_R=-\frac{1+\frac{R_4}{S_4}}{\left(1+\frac{S_2}{R_2}\right)\frac{S_3}{R_3}}}$			${\displaystyle i_1=1+\frac{R_4}{S_4}}$		${\displaystyle i_2=\frac{1+\frac{R_4}{S_4}}{1+\frac{S_2}{R_2}}}$			${\displaystyle i_{10}=\frac{1}{1+\frac{S_2}{R_2}}}$
Ratio 3–4 & 9 Ordinary[ad] Elementary Noted[ae]	${\displaystyle i_3=\frac{(S_1+R_1)(S_4+R_4)}{S_1(S_4+R_4)+S_4{R}_1}}$					${\displaystyle i_4=1+\frac{S_2{R}_1}{S_1(S_2+R_2)}}$			${\displaystyle i_9=\frac{R_2(S_4+R_4)}{R_2(S_4+R_4)+S_2{R}_4}}$
	${\displaystyle i_3=\frac{1}{\frac{1}{1+\frac{R_1}{S_1}}+\frac{1}{\left(1+\frac{S_1}{R_1}\right)\left(1+\frac{R_4}{S_4}\right)}}}$					${\displaystyle i_4=1+\frac{\frac{R_1}{S_1}}{1+\frac{R_2}{S_2}}}$			${\displaystyle i_9=\frac{1}{1+\frac{\frac{S_2}{R_2}}{1+\frac{S_4}{R_4}}}}$
Ratio 5 & 8 Elementary Noted[ae]	${\displaystyle i_5=\frac{(S_1(S_2+R_2)+R_1{S}_2)(S_4+R_4)}{S_1(S_2+R_2)(S_4+R_4)+R_1{S}_2{S}_4}}$						${\displaystyle i_8=\frac{R_2(S_3+R_3)(S_4+R_4)}{R_2(S_3+R_3)(S_4+R_4)+S_2{S}_3{R}_4}}$
	${\displaystyle i_5=\frac{1}{\frac{1}{1+\frac{\frac{R_1}{S_1}}{1+\frac{R_2}{S_2}}}+\frac{1}{\left(1+\frac{S_1}{R_1}\left(1+\frac{R_2}{S_2}\right)\right)\left(1+\frac{R_4}{S_4}\right)}}}$						${\displaystyle i_8=\frac{1}{1+\frac{1}{\frac{R_2}{S_2}\left(1+\frac{R_3}{S_3}\right)\left(1+\frac{S_4}{R_4}\right)}}}$
Ratio 6 & 7 Ordinary[ad] Elementary Noted[ae]	${\displaystyle i_6=\frac{(S_1{R}_2(S_3+R_3)+S_2{S}_3(S_1+R_1))(S_4+R_4)}{(S_1{R}_2(S_3+R_3)+S_1{S}_2{S}_3)(S_4+R_4)+R_1{S}_2{S}_3{S}_4}}$									${\displaystyle i_7=\frac{1}{1}}$
	${\displaystyle i_6=\frac{1}{1+\frac{\frac{S_2}{R_2}}{1+\frac{R_3}{S_3}}\left(1+\frac{\frac{R_1}{S_1}}{1+\frac{R_4}{S_4}}\right)}+\frac{1}{\frac{1+\frac{R_2}{S_2}\left(1+\frac{R_3}{S_3}\right)}{1+\frac{R_1}{S_1}}+\frac{1}{\left(1+\frac{S_1}{R_1}\right)\left(1+\frac{R_4}{S_4}\right)}}}$
Kinetic Ratios
Specific Torque[u] R–2 & 10	${\displaystyle \frac{T_{2;R}}{T_{1;R}}=-\frac{1+\frac{R_4}{S_4}{\eta }_0}{\left(1+\frac{S_2}{R_2}\cdot \frac{1}{{\eta }_0}\right)\frac{S_3}{R_3}\cdot \frac{1}{{\eta }_0}}}$			${\displaystyle \frac{T_{2;1}}{T_{1;1}}=1+\frac{R_4}{S_4}{\eta }_0}$		${\displaystyle \frac{T_{2;2}}{T_{1;2}}=\frac{1+\frac{R_4}{S_4}{\eta }_0}{1+\frac{S_2}{R_2}\cdot \frac{1}{{\eta }_0}}}$			${\displaystyle \frac{T_{2;10}}{T_{1;10}}=\frac{1}{1+\frac{S_2}{R_2}\cdot \frac{1}{{\eta }_0}}}$
Specific Torque[u] 3–4 & 9	${\displaystyle \frac{T_{2;3}}{T_{1;3}}=\frac{1}{\frac{1}{1+\frac{R_1}{S_1}{{\eta }_0}^{\frac{1}{2}}}+\frac{1}{\left(1+\frac{S_1}{R_1}{{\eta }_0}^{\frac{1}{2}}\right)\left(1+\frac{R_4}{S_4}{\eta }_0\right)}}}$					${\displaystyle \frac{T_{2;4}}{T_{1;4}}=1+\frac{\frac{R_1}{S_1}{\eta }_0}{1+\frac{R_2}{S_2}\cdot \frac{1}{{\eta }_0}}}$			${\displaystyle \frac{T_{2;9}}{T_{1;9}}=\frac{1}{1+\frac{\frac{S_2}{R_2}\cdot \frac{1}{{\eta }_0}}{1+\frac{S_4}{R_4}{\eta }_0}}}$
Specific Torque[u] 5 & 8	${\displaystyle \frac{T_{2;5}}{T_{1;5}}=\frac{1}{\frac{1}{1+\frac{\frac{R_1}{S_1}{{\eta }_0}^{\frac{1}{2}}}{1+\frac{R_2}{S_2}\cdot \frac{1}{{{\eta }_0}^{\frac{1}{2}}}}}+\frac{1}{\left(1+\frac{S_1}{R_1}{{\eta }_0}^{\frac{1}{2}}\left(1+\frac{R_2}{S_2}{{\eta }_0}^{\frac{1}{2}}\right)\right)\left(1+\frac{R_4}{S_4}{\eta }_0\right)}}}$						${\displaystyle \frac{T_{2;8}}{T_{1;8}}=\frac{1}{1+\frac{1}{\frac{R_2}{S_2}{\eta }_0\left(1+\frac{R_3}{S_3}{\eta }_0\right)\left(1+\frac{S_4}{R_4}{\eta }_0\right)}}}$
Specific Torque[u] 6 & 7	${\displaystyle \frac{T_{2;6}}{T_{1;6}}=\frac{1}{1+\frac{\frac{S_2}{R_2}\cdot \frac{1}{{{\eta }_0}^{\frac{1}{2}}}}{1+\frac{R_3}{S_3}{{\eta }_0}^{\frac{1}{2}}}\left(1+\frac{\frac{R_1}{S_1}\cdot \frac{1}{{{\eta }_0}^{\frac{1}{3}}}}{1+\frac{R_4}{S_4}{{\eta }_0}^{\frac{1}{2}}}\right)}+\frac{1}{\frac{1+\frac{R_2}{S_2}\cdot \frac{1}{{{\eta }_0}^{\frac{1}{2}}}\left(1+\frac{R_3}{S_3}\cdot \frac{1}{{{\eta }_0}^{\frac{1}{2}}}\right)}{1+\frac{R_1}{S_1}{{\eta }_0}^{\frac{1}{3}}}+\frac{1}{\left(1+\frac{S_1}{R_1}{{\eta }_0}^{\frac{1}{3}}\right)\left(1+\frac{R_4}{S_4}{{\eta }_0}^{\frac{1}{2}}\right)}}}$									${\displaystyle \frac{T_{2;7}}{T_{1;7}}=\frac{1}{1}}$
^Revised 14 October 2025 ^Layout Input and output are on opposite sides Planetary gearset 1 is on the input (turbine) side Input shafts areC2 (planetary gear carrier of gearset 2) and, if actuated,R3 andS4 Output shaft isC4 (planetary gear carrier of gearset 4) ^Total Ratio Span (Total Gear/Transmission Ratio) Nominal ${\displaystyle \frac{i_1}{i_n}}$ 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 ^Total Ratio Span (Total Gear/Transmission Ratio) Effective ${\displaystyle \frac{min(i_1;|i_R|)}{i_n}}$ The span is only effective to the extent that the reverse gear ratio corresponds to that of 1st gear see alsoStandard R:1 ^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 ^Average Gear Step ${\displaystyle {\left(\frac{i_1}{i_n}\right)}^{\frac{1}{n-1}}}$ With decreasing step width the gears connect better to each other shifting comfort increases ^Sun 1: sun gear of gearset 1 ^Ring 1: ring gear of gearset 1 ^Sun 2: sun gear of gearset 2 ^Ring 2: ring gear of gearset 2 ^Sun 3: sun gear of gearset 3 ^Ring 3: ring gear of gearset 3 ^Sun 4: sun gear of gearset 4 ^Ring 4: ring gear of gearset 4 ^abcdefghijklmnopqrstuvwxyzaaabacadaeafagahaiajakalStandard 50:50 — 50 % Is Above And 50 % Is Below The Average Gear Step — With steadily decreasing gear steps (yellow highlighted lineStep) and a particularly large step from 1st to 2nd gear thelower half of the gear steps (between the small gears; rounded down, here the first 4)is always larger and theupper half of the gear steps (between the large gears; rounded up, here the last 5)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) ^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) ^Standard 1:2 — Gear Step 1st To 2nd Gear As Small As Possible — With continuously decreasing gear steps (yellow marked lineStep) thelargest 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) ^abcdeFrom large to small gears (from right to left) ^abcdefghijklmnopqrstuvwxyzaaabacadaeStandard STEP — From Large To Small Gears: Steady And Progressive Increase In Gear Steps — Gear steps should increase: Δ Step (first green highlighted lineΔ Step) is always greater than 1 Asprogressive as possible: Δ Step is always greater than the previous step Not progressively increasing is acceptable (red) Not increasing is unsatisfactory (bold) ^abcdefghijklmnopqrstuvwxyzaaabacadaeafagStandard SPEED — From Small To Large Gears: Steady Increase In Shaft Speed Difference — Shaft speed differences should increase: Δ Shaft Speed (second line marked in greenΔ (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) ^abcdefghijklmnSpecific Torque Ratio And Efficiency The specific torque is the Ratio of output torque${\displaystyle T_{2;n}}$ to input torque${\displaystyle T_{1;n}}$ with${\displaystyle n=gear}$ Theefficiency is calculated from the specific torque in relation to the transmission ratio 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 ^abcdefghijkCorridor for specific torque 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${\displaystyle {{\eta }_0}^{\frac{1}{2}}}$ at${\displaystyle {0.9800}^{\frac{1}{2}}=0.98995}$ (upper value) and${\displaystyle {0.9700}^{\frac{1}{2}}=0.98489}$ (lower value) ^Permanentlycoupled elements S1 andS2 C1 (carrier 1) andR4 R2 andS3 R3 andS4 ^Blockss1 ^BlocksR1 ^CouplesR2 andS3 with the dedicated intermediate shaft ^CouplesC3 (carrier 3) with the dedicated intermediate shaft ^CouplesR3 andS4 with the input shaft ^CouplesC1 (carrier 1) andR4 with the dedicated intermediate shaft ^abcOrdinary Noted For direct determination of the ratio ^abcdElementary 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