ZF 8HP transmission

The 8HP 70 transmission with the gearset 4 in 23-85-teeth-configuration was the pilot series and therefore without generation designation. It was first used in the BMW 7 Series (F01) 760Li, has a torque handling limit of 700 N⋅m (516 lb⋅ft), and weighs 87 kg (192 lb).^[11]

In addition to the rear-wheel drive variant, two different four-wheel drive versions were available, with a version destined for Volkswagen Group applications using a Torsen centre differential.^[12] It is able to encompass a torque range from 300 N⋅m (221 lb⋅ft) to 1,000 N⋅m (738 lb⋅ft), and is available for use in middle-class cars through to large luxury sport utility vehicles.^[12]

Since gearset 4 meshes in almost all gears up to and including 5th gear, large gear wheels are advantageous for durability. As the very high ratio 1st gear is formed exclusively by gearset 4, its sun gear is unusually small. For this reason, this gearset was enlarged by over 20% when the 1st generation was introduced, even if this advantage had to be given up again immediately when the 2nd generation was introduced in order to increase the total span.

Efficiency improvements over the pilot design and the first generation include a wider ratio span of 7.81, reduced drag torque from the shift elements, reduction in required oil pump pressure, and broadened use of the coasting and start-stop systems.^[13] ZF estimated fuel economy improvement over first generation to be 3%. Refinements were also made with respect to vibration.

Major improvements are total span of 8.59 and a fuel economy improvement of 2.5% compared to the second generation. There are several options in maximum torque available, also the gearbox is available with mild hybrid and plug in hybrid options: With 15 kW (20 hp) and 200 N⋅m (148 lb⋅ft) supporting boosting and recuperation in combination with 48 Volt technology up to 90 kW (121 hp) and 250 N⋅m (184 lb⋅ft) for usage with higher voltage.^[14]

Major improvement is the transition to a versatile modular system that allows vehicle manufacturers to comprehensively and flexibly electrify their models as required. Plug-in Hybrid options with up to 160 kW (215 hp) and 280 N⋅m (207 lb⋅ft) are capable of saving up to 70% of carbon emissions compared with a purely conventional variant of the 8HP according to the Worldwide Harmonised Light Vehicles Test Procedure (WLTP).^[8] In addition, a modification to gearset 3 increased the reverse gear ratio, making it less disadvantageous. With this gearset concept, the already disadvantageously large step from 7th to 8th gear is further increased, albeit only slightly.

The main objective in replacing the predecessor model was to improve vehicle fuel economy with extra speeds and a wider gear span to allow the engine speed level to be lowered (downspeeding). Compared to the 6-speed ZF 6HP transmission it uses 12% less fuel, and 14% less than a 5-speed transmission.^[15][16] Due to changes in internal design, the shift times have reduced to 0.2 seconds; additionally, the unit brings the ability to shift in a non-sequential manner – going from gear 8 to gear 2 in extreme situations simply by changing one shift element (actuating brake B and releasing clutch D).^[17]

In order to increase the number of ratios, ZF has abandoned the conventional design method of limiting themselves to pure in-line epicyclic gearing and extended it to a combination with parallel epicyclic gearing. This was only possible thanks to computer-aided design and has resulted in a globally patented gearset concept. The resulting progress is reflected in a better ratio of the number of gears to the number of components used compared to existing layouts. The 8HP has become the new reference standard (benchmark) for automatic transmissions.

Gearset Concept: Cost-Effectiveness^[a]

With Assessment	Output: Gear Ratios	Innovation Elasticity[b] Δ Output : Δ Input	Input: Main Components
			Total	Gearsets	Brakes	Clutches
8HP 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 ${\displaystyle {\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}$	${\displaystyle {\tfrac {n_{G1}-n_{G2}}{n_{G2}}}}$	${\displaystyle {\tfrac {n_{B1}-n_{B2}}{n_{B2}}}}$	${\displaystyle {\tfrac {n_{C1}-n_{C2}}{n_{C2}}}}$
8HP 6HP[c]	8[d] 6[d]	Progress[b]	9 8	4 3[e]	2 2	3 3
Δ Number	2		1	1	0	0
Relative Δ	0.333 ${\displaystyle {\tfrac {2}{6}}}$	2.667[b] ${\displaystyle {\tfrac {2}{6}}:{\tfrac {1}{8}}={\tfrac {1}{3}}\cdot {\tfrac {8}{1}}={\tfrac {8}{3}}}$	0.125 ${\displaystyle {\tfrac {1}{8}}}$	0.333 ${\displaystyle {\tfrac {1}{3}}}$	0.000 ${\displaystyle {\tfrac {0}{2}}}$	0.000 ${\displaystyle {\tfrac {0}{3}}}$
8HP 3-Speed[f]	8[d] 3[d]	Market Position[b]	9 7	4 2	2 3	3 2
Δ Number	5		2	2	-1	1
Relative Δ	1.667 ${\displaystyle {\tfrac {5}{3}}}$	5.833[b] ${\displaystyle {\tfrac {5}{3}}:{\tfrac {2}{7}}={\tfrac {5}{3}}\cdot {\tfrac {7}{2}}={\tfrac {35}{6}}}$	0.286 ${\displaystyle {\tfrac {2}{7}}}$	1.000 ${\displaystyle {\tfrac {1}{1}}}$	−0.333 ${\displaystyle {\tfrac {-1}{3}}}$	0.500 ${\displaystyle {\tfrac {1}{2}}}$
^ 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 ^ a b c d e 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) ^ Direct Predecessor To reflect the progress of the specific model change ^ a b c d plus 1 reverse gear ^ of which 2 gearsets are combined as a compound Ravigneaux gearset ^ 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

The ratios of the 8 gears are relatively unevenly distributed in all versions. Particularly noticeable are

• the too small step between 3rd and 4th gear
• and the too large step between 7th and 8th gear.

This cannot be eliminated without affecting all other gear ratios. On the other hand the selected gearset concept offers 2 to 3 gears more than conventional transmissions of comparable manufacturing costs, which more than compensates for the weaknesses.

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]
									Avg.[i]
Model Type	Version		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	6	7	8
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]	${\displaystyle {i_{6}}}$[b]	${\displaystyle {i_{7}}}$[b]	${\displaystyle {i_{8}}}$[b]
Step[r]	${\displaystyle -{\frac {i_{R}}{i_{1}}}}$[s]	${\displaystyle {\frac {i_{1}}{i_{1}}}}$	${\displaystyle {\frac {i_{1}}{i_{2}}}}$[t]	${\displaystyle {\frac {i_{2}}{i_{3}}}}$	${\displaystyle {\frac {i_{3}}{i_{4}}}}$	${\displaystyle {\frac {i_{4}}{i_{5}}}}$	${\displaystyle {\frac {i_{5}}{i_{6}}}}$	${\displaystyle {\frac {i_{6}}{i_{7}}}}$	${\displaystyle {\frac {i_{7}}{i_{8}}}}$
Δ Step[u][v]			${\displaystyle {\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}}$	${\displaystyle {\tfrac {i_{2}}{i_{3}}}:{\tfrac {i_{3}}{i_{4}}}}$	${\displaystyle {\tfrac {i_{3}}{i_{4}}}:{\tfrac {i_{4}}{i_{5}}}}$	${\displaystyle {\tfrac {i_{4}}{i_{5}}}:{\tfrac {i_{5}}{i_{6}}}}$	${\displaystyle {\tfrac {i_{5}}{i_{6}}}:{\tfrac {i_{6}}{i_{7}}}}$	${\displaystyle {\tfrac {i_{6}}{i_{7}}}:{\tfrac {i_{7}}{i_{8}}}}$
Shaft Speed	${\displaystyle {\frac {i_{1}}{i_{R}}}}$	${\displaystyle {\frac {i_{1}}{i_{1}}}}$	${\displaystyle {\frac {i_{1}}{i_{2}}}}$	${\displaystyle {\frac {i_{1}}{i_{3}}}}$	${\displaystyle {\frac {i_{1}}{i_{4}}}}$	${\displaystyle {\frac {i_{1}}{i_{5}}}}$	${\displaystyle {\frac {i_{1}}{i_{6}}}}$	${\displaystyle {\frac {i_{1}}{i_{7}}}}$	${\displaystyle {\frac {i_{1}}{i_{8}}}}$
Δ Shaft Speed[w]	${\displaystyle 0-{\tfrac {i_{1}}{i_{R}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{1}}}-0}$	${\displaystyle {\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{4}}}-{\tfrac {i_{1}}{i_{3}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{5}}}-{\tfrac {i_{1}}{i_{4}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{6}}}-{\tfrac {i_{1}}{i_{5}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{7}}}-{\tfrac {i_{1}}{i_{6}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{8}}}-{\tfrac {i_{1}}{i_{7}}}}$
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]	${\displaystyle \mu _{6}}$[c]	${\displaystyle \mu _{7}}$[c]	${\displaystyle \mu _{8}}$[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]	${\displaystyle {\frac {\mu _{6}}{i_{6}}}}$[d]	${\displaystyle {\frac {\mu _{7}}{i_{7}}}}$[d]	${\displaystyle {\frac {\mu _{8}}{i_{8}}}}$[d]
2008: Pilot Series
8HP 70[x]	700 N⋅m (516 lb⋅ft)		48[18] 96	48[18] 96	69[6] 111	23[6] 85	2 3	7.0435 4.9452 [g][s]	1.7693
									1.3216[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.2968 [s][g] ${\displaystyle -{\tfrac {1,744}{529}}}$	4.6957 ${\displaystyle {\tfrac {108}{23}}}$	3.1304[v] ${\displaystyle {\tfrac {72}{23}}}$	2.1039 ${\displaystyle {\tfrac {162}{77}}}$	1.6667 [r][v][w] ${\displaystyle {\tfrac {5}{3}}}$	1.2845[v] ${\displaystyle {\tfrac {8,826}{6,871}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8392 [v][w] ${\displaystyle {\tfrac {120}{143}}}$	0.6667 ${\displaystyle {\tfrac {2}{3}}}$
Step	0.7021[s]	1.0000	1.5000	1.4879	1.2623[r]	1.2975	1.2845	1.1917	1.2587
Δ Step[u]			1.0081[v]	1.1787	0.9729[v]	1.0101[v]	1.0779	0.9467[v]
Speed	-1.4243	1.0000	1.5000	2.2319	2.8174	3.6555	4.6957	5.5957	7.0435
Δ Speed	1.4243	1.0000	0.5000	0.7319	0.5855[w]	0.8382	1.0401	0.9000[w]	1.4478
Torque Ratio[c]	–3.1186 –3.0313	4.6217 4.5848	3.0603 3.0253	2.0820 2.0709	1.6446 1.6336	1.2720 1.2658	1.0000	0.8347 0.8324	0.6622 0.6599
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9460 0.9195	0.9843 0.9764	0.9776 0.9664	0.9896 0.9843	0.9867 0.9802	0.9903 0.9854	1.0000	0.9947 0.9920	0.9932 0.9898
2010: 1st Generation
HP 30/I 8HP 45	300 N⋅m (221 lb⋅ft) 450 N⋅m (332 lb⋅ft)		48 96	48 96	60 96	28 104	2 3	7.0714 4.9429 [g][s]	1.7728
									1.3224[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.2952 [s][g] ${\displaystyle -{\tfrac {346}{105}}}$	4.7143 ${\displaystyle {\tfrac {33}{7}}}$	3.1429[v] ${\displaystyle {\tfrac {22}{7}}}$	2.1064 ${\displaystyle {\tfrac {99}{47}}}$	1.6667 [r][v][w] ${\displaystyle {\tfrac {5}{3}}}$	1.2854[v] ${\displaystyle {\tfrac {1,171}{911}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8387 [v][w] ${\displaystyle {\tfrac {26}{31}}}$	0.6667 ${\displaystyle {\tfrac {2}{3}}}$
Step	0.6990[s]	1.0000	1.5000	1.4921	1.2638[r]	1.2966	1.2854	1.1923	1.2581
Δ Step[u]			1.0053[v]	1.1805	0.9747[v]	1.0087[v]	1.0781	0.9477[v]
Speed	-1.4306	1.0000	1.5000	2.2381	2.8286	3.6576	4.7143	5.6209	7.0714
Δ Speed	1.4306	1.0000	0.5000	0.7381	0.5905[w]	0.8390	1.0467	0.9066[w]	1.45058
Torque Ratio[c]	–3.1171 –3.0299	4.6400 4.6029	3.0724 3.0373	2.0844 2.0734	1.6446 1.6336	1.2729 1.2666	1.0000	0.8343 0.8320	0.6622 0.6599
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9460 0.9195	0.9842 0.9764	0.9776 0.9664	0.9896 0.9843	0.9867 0.9802	0.9903 0.9854	1.0000	0.9944 0.9915	0.9943 0.9913
8HP 55 8HP 65 8HP 70 8HP 90	650 N⋅m (479 lb⋅ft) 650 N⋅m (479 lb⋅ft) 700 N⋅m (516 lb⋅ft) 900 N⋅m (664 lb⋅ft)		48 [18][19] 96	48 [18][19] 96	69 111	28 104	2 3	7.0714 4.9752 [g][s]	1.7728
									1.3224[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.3168 [s][g] ${\displaystyle -{\tfrac {534}{161}}}$	4.7143 ${\displaystyle {\tfrac {33}{7}}}$	3.1429[v] ${\displaystyle {\tfrac {22}{7}}}$	2.1064 ${\displaystyle {\tfrac {99}{47}}}$	1.6667 [r][v][w] ${\displaystyle {\tfrac {5}{3}}}$	1.2847[v] ${\displaystyle {\tfrac {5,397}{4,201}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8392 [v][w] ${\displaystyle {\tfrac {120}{143}}}$	0.6667 ${\displaystyle {\tfrac {2}{3}}}$
Step	0.7036[s]	1.0000	1.5000	1.4921	1.2638[r]	1.2973	1.2847	1.1917	1.2587
Δ Step[u]			1.0053[v]	1.1806	0.9742[v]	1.0098[v]	1.0781	0.9467[v]
Speed	-1.4213	1.0000	1.5000	2.2381	2.8286	3.6696	4.7143	5.6179	7.0714
Δ Speed	1.4243	1.0000	0.5000	0.7381	0.5905[w]	0.8410	1.0447	0.9036[w]	1.4536
Torque Ratio[c]	–3.1377 –3.0499	4.6400 4.6029	3.0724 3.0373	2.0844 2.0734	1.6446 1.6336	1.2722 1.2660	1.0000	0.8347 0.8324	0.6622 0.6599
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9460 0.9195	0.9842 0.9764	0.9776 0.9664	0.9896 0.9843	0.9867 0.9802	0.9903 0.9854	1.0000	0.9947 0.9920	0.9932 0.9898
2014: 2nd Generation
8HP 75/I	740 N⋅m (546 lb⋅ft)[7]		48 96	48 96	69 111	28 104	2 3	7.0714 4.9752 [g][s]	1.7728
									1.3224[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.3168 [s][g]	4.7143	3.1429[v]	2.1064	1.6667 [r][v][w]	1.2847[v]	1.0000	0.8392 [v][w]	0.6667
8HP 30/II 8HP 50	300 N⋅m (221 lb⋅ft)[7] 500 N⋅m (369 lb⋅ft)[7]		48 96	54 96	60 96	24 96	2 3	7.8125 5.1840 [g][s]	1.7889
									1.3413[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.4560[s] ${\displaystyle -{\tfrac {432}{125}}}$	5.0000 ${\displaystyle {\tfrac {5}{1}}}$	3.2000[v] ${\displaystyle {\tfrac {16}{5}}}$	2.1429 ${\displaystyle {\tfrac {15}{7}}}$	1.7200 [r][v][w] ${\displaystyle {\tfrac {43}{25}}}$	1.3139[v] ${\displaystyle {\tfrac {1,507}{1,147}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8221 [v][w] ${\displaystyle {\tfrac {208}{253}}}$	0.6400 ${\displaystyle {\tfrac {16}{25}}}$
Step	0.6912[s]	1.0000	1.5625	1.4933	1.2458[r]	1.3091	1.3139	1.2163	1.2846
Δ Step[u]			1.0463[v]	1.1986	0.9517[v]	0.9964[v]	1.0802	0.9469[v]
Speed	-1.4468	1.0000	1.5625	2.3333	2.9070	3.8056	5.0000	6.0817	7.8125
Δ Speed	1.4468	1.0000	0.5625	0.7708	0.5736[w]	0.8986	1.1944	1.0817[w]	1.7308
Torque Ratio[c]	–3.2698 –3.1785	4.9200 4.8800	3.1258 3.0888	2.1207 2.1096	1.6965 1.6848	1.3008 1.2943	1.0000	0.8873 0.8148	0.6353 0.6330
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9461 0.9197	0.9840 0.9760	0.9768 0.9653	0.9897 0.9845	0.9863 0.9796	0.9901 0.9851	1.0000	0.9941 0.9911	0.9927 0.9890
8HP 75/II 8HP 95	740 N⋅m (546 lb⋅ft)[7] 900 N⋅m (664 lb⋅ft)[y]		48 96	54 96	69 111	24 96	2 3	7.8125 2.2261 [g][s]	1.7889
									1.3413[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.4783 [s][g] ${\displaystyle -{\tfrac {80}{23}}}$	5.0000 ${\displaystyle {\tfrac {5}{1}}}$	3.2000[v] ${\displaystyle {\tfrac {16}{5}}}$	2.1429 ${\displaystyle {\tfrac {15}{7}}}$	1.7200 [r][v][w] ${\displaystyle {\tfrac {43}{25}}}$	1.3131[v] ${\displaystyle {\tfrac {2,315}{1,763}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8226 [v][w] ${\displaystyle {\tfrac {320}{389}}}$	0.6400 ${\displaystyle {\tfrac {16}{25}}}$
Step	0.6957[s]	1.0000	1.5625	1.4933	1.2458[r]	1.3099	1.3131	1.2156	1.2853
Δ Step[u]			1.0463[v]	1.1986	0.9511[v]	0.9975[v]	1.0802	0.9458[v]
Speed	-1.4375	1.0000	1.5625	2.3333	2.9070	3.8078	5.0000	6.0781	7.8125
Δ Speed	1.4375	1.0000	0.5625	0.7708	0.5736[w]	0.9008	1.1922	1.0781[w]	1.7344
Torque Ratio[c]	–3.2910 –3.1993	4.9200 4.8800	3.1258 3.0888	2.1207 2.1096	1.6965 1.6848	1.3001 1.2935	1.0000	0.8178 0.8153	0.6353 0.6330
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9462 0.9198	0.9840 0.9760	0.9768 0.9653	0.9897 0.9845	0.9863 0.9796	0.9901 0.9851	1.0000	0.9942 0.9911	0.9927 0.9890
2018: 3rd Generation
8HP 76/I	760 N⋅m (561 lb⋅ft)[z]		48 96	54 96	69 111	24 96	2 3	7.8125 5.4348 [g][s]	1.7889
									1.3413[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.4783 [s][g]	5.0000	3.2000[v]	2.1429	1.7200 [r][v][w]	1.3131[v]	1.0000	0.8226 [v][w]	0.6400
8HP 30/III 8HP 51	300 N⋅m (221 lb⋅ft)[aa] 500 N⋅m (369 lb⋅ft)[ab]		48 96	54 96	60 96	24 102	2 3	8.2031 5.8000 [g][s]	1.8330
									1.3507[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.7120 [s][g] ${\displaystyle -{\tfrac {464}{125}}}$	5.2500 ${\displaystyle {\tfrac {21}{4}}}$	3.3600[v] ${\displaystyle {\tfrac {84}{25}}}$	2.1724 ${\displaystyle {\tfrac {63}{29}}}$	1.7200 [r][v][w] ${\displaystyle {\tfrac {43}{25}}}$	1.3161[v] ${\displaystyle {\tfrac {6,371}{4,841}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8221 [v][w] ${\displaystyle {\tfrac {208}{253}}}$	0.6400 ${\displaystyle {\tfrac {16}{25}}}$
Step	0.7070[s]	1.0000	1.5625	1.5467	1.2630[r]	1.3069	1.3161	1.2163	1.2846
Δ Step[u]			1.0102[v]	1.2246	0.9664[v]	0.9931[v]	1.0820	0.9469[v]
Speed	-1.4143	1.0000	1.5625	2.4167	3.0523	3.9892	5.2500	6.3858	8.2031
Δ Speed	1.4143	1.0000	0.5625	0.8542	0.6357[w]	0.9369	1.2608	1.1358[w]	1.8173
Torque Ratio[c]	–3.5138 –3.4168	5.1650 5.1225	3.2815 3.2423	2.1501 2.1389	1.6965 1.6848	1.3031 1.2966	1.0000	0.8173 0.8148	0.6353 0.6330
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9466 0.9205	0.9838 0.9757	0.9766 0.9650	0.9897 0.9846	0.9863 0.9796	0.9902 0.9852	1.0000	0.9941 0.9911	0.9927 0.9890
8HP 76/II	760 N⋅m (561 lb⋅ft)[ac]		48 96	54 96	69 111	24 108	2 3	8.5938 6.2391 [g][s]	1.8762
									1.3597[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.9930 [s][g] ${\displaystyle -{\tfrac {2,296}{575}}}$	5.5000 ${\displaystyle {\tfrac {11}{2}}}$	3.5200[v] ${\displaystyle {\tfrac {88}{25}}}$	2.2000 ${\displaystyle {\tfrac {11}{5}}}$	1.7200 [r][v][w] ${\displaystyle {\tfrac {43}{25}}}$	1.3172[v] ${\displaystyle {\tfrac {191}{145}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8226 [v][w] ${\displaystyle {\tfrac {320}{389}}}$	0.6400 ${\displaystyle {\tfrac {16}{25}}}$
Step	0.7260[s]	1.0000	1.5625	1.6000	1.2791[r]	1.3058	1.3172	1.2156	1.2853
Δ Step[u]			0.9766[v]	1.2509	0.9796[v]	0.9913[v]	1.0836	0.9458[v]
Speed	-1.3774	1.0000	1.5625	2.5000	3.1977	4.1754	5.5000	6.6859	8.5938
Δ Speed	1.3774	1.0000	0.5625	0.9375	0.6977[w]	0.9777	1.3246	1.1859[w]	1.8321
Torque Ratio[c]	–3.7818 –3.6783	5.4100 5.3650	3.4371 3.3958	2.1776 2.1663	1.6965 1.6848	1.3044 1.2979	1.0000	0.8178 0.8153	0.6353 0.6330
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9471 0.9212	0.9836 0.9755	0.9765 0.9647	0.9898 0.9847	0.9863 0.9796	0.9902 0.9853	1.0000	0.9942 0.9911	0.9927 0.9890
2022: 4th Generation
8HP 100	1,000 N⋅m (738 lb⋅ft) [ad][8]		48 96	54 96	60 108	24 96	2 3	7.8125 6.2000 [g][s]	1.7889
									1.3413[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.9680 [s][g] ${\displaystyle -{\tfrac {496}{125}}}$	5.0000 ${\displaystyle {\tfrac {5}{1}}}$	3.2000[v] ${\displaystyle {\tfrac {16}{5}}}$	2.1429 ${\displaystyle {\tfrac {15}{7}}}$	1.7200 [r][v][w] ${\displaystyle {\tfrac {43}{25}}}$	1.2973[v] ${\displaystyle {\tfrac {1,571}{1,211}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8327 [v][w] ${\displaystyle {\tfrac {224}{269}}}$	0.6400 ${\displaystyle {\tfrac {16}{25}}}$
Step	0.7936[s]	1.0000	1.5625	1.4933	1.2458[r]	1.3259	1.2973	1.2009	1.3011
Δ Step[u]			1.0463[v]	1.1986	0.9397[v]	1.0220[v]	1.0803	0.9230[v]
Speed	-1.2601	1.0000	1.5625	2.3333	2.9070	3.8542	5.0000	6.0045	7.8125
Δ Speed	1.2601	1.0000	0.5625	0.7708	0.5736[w]	0.9473	1.1458	1.0045[w]	1.8080
Torque Ratio[c]	–3.7579 –3.6550	4.9200 4.8800	3.1258 3.0888	2.1207 2.1096	1.6965 1.6848	1.2846 1.2782	1.0000	0.8280 0.8256	0.6353 0.6330
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9471 0.9211	0.9840 0.9760	0.9768 0.9653	0.9897 0.9845	0.9863 0.9796	0.9902 0.9853	1.0000	0.9944 0.9915	0.9927 0.9890
8HP 80	800 N⋅m (590 lb⋅ft) [8][ae]		48 96	54 96	60 108	24 108	2 3	8.5938 7.1000 [g][s]	1.8762
									1.3597[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−4.5440 [s][g] ${\displaystyle -{\tfrac {1,704}{375}}}$	5.5000 ${\displaystyle {\tfrac {11}{2}}}$	3.5200[v] ${\displaystyle {\tfrac {88}{25}}}$	2.2000 ${\displaystyle {\tfrac {11}{5}}}$	1.7200 [r][v][w] ${\displaystyle {\tfrac {43}{25}}}$	1.3010[v] ${\displaystyle {\tfrac {389}{299}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8327 [v][w] ${\displaystyle {\tfrac {224}{269}}}$	0.6400 ${\displaystyle {\tfrac {16}{25}}}$
Step	0.8262[s]	1.0000	1.5625	1.6000	1.2791[r]	1.3221	1.3010	1.2009	1.3011
Δ Step[u]			0.9766[v]	1.2509	0.9675[v]	1.0162[v]	1.0834	0.9230[v]
Speed	-1.2104	1.0000	1.5625	2.5000	3.1977	4.2275	5.5000	6.6049	8.5938
Δ Speed	1.2104	1.0000	0.5625	0.9375	0.6977[w]	1.0298	1.2725	1.1049[w]	1.9888
Torque Ratio[c]	–4.3071 –4.1910	5.4100 5.3650	3.4371 3.3958	2.1776 2.1663	1.6965 1.6848	1.2885 1.2822	1.0000	0.8280 0.8256	0.6353 0.6330
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9479 0.9223	0.9836 0.9755	0.9765 0.9647	0.9898 0.9847	0.9863 0.9796	0.9904 0.9856	1.0000	0.9944 0.9915	0.9927 0.9890
2016: Racing Cars
8P 45R[af]	450 N⋅m (332 lb⋅ft) – 1,050 N⋅m (774 lb⋅ft)[9]		TBD	TBD	60 96	TBD	2 3	4.2000 TBD	TBD
									1.2275[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	TBD	TBD	TBD	TBD	TBD	TBD	1.0000	TBD	TBD
2017: Commercial Vehicles[ag]
8AP 600 T[ah] 8AP 800 T 8AP 1000 T 8AP 1200 T	600 N⋅m (443 lb⋅ft) 800 N⋅m (590 lb⋅ft) 1,000 N⋅m (738 lb⋅ft) 1,200 N⋅m (885 lb⋅ft)[ai]		65[aj] 115	65[aj] 115	62 122	27 105	2 3	7.6522 6.6523 [g][s]	1.7673
									1.3374[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−4.2501 [s][g] ${\displaystyle -{\tfrac {10,672}{2,511}}}$	4.8889 ${\displaystyle {\tfrac {44}{9}}}$	3.1235[v] ${\displaystyle {\tfrac {253}{81}}}$	2.0334 ${\displaystyle {\tfrac {1,584}{779}}}$	1.6389 [r][v][w] ${\displaystyle {\tfrac {59}{36}}}$	1.2541[v] ${\displaystyle {\tfrac {123,164}{98,209}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8400 [v][w] ${\displaystyle {\tfrac {2,116}{2,519}}}$	0.6389 ${\displaystyle {\tfrac {23}{36}}}$
Step	0.8693[s]	1.0000	1.5652	1.5361	1.2407[r]	1.3068	1.2541	1.1905	1.3148
Δ Step[u]			1.0190[v]	1.2381	0.9494[v]	1.0420[v]	1.0535	0.9054[v]
Speed	-1.1503	1.0000	1.5652	2.4043	2.9831	3.8983	4.8889	5.8200	7.6522
Δ Speed	1.1503	1.0000	0.5652	0.8391	0.5787[w]	0.9153	0.9906	0.9311[w]	1.8322
Torque Ratio[c]	–4.0268 –3.9174	4.8111 4.7722	3.0513 3.0152	2.0132 2.0030	1.6181 1.6077	1.2424 1.2365	1.0000	0.8355 0.8331	0.6342 0.6318
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9475 0.9217	0.9841 0.9761	0.9769 0.9654	0.9901 0.9851	0.9873 0.9810	0.9907 0.9860	1.0000	0.9946 0.9918	0.9927 0.9890
8AP 1200 S [ak]	1,200 N⋅m (885 lb⋅ft)[ai]		65[aj] 115	65[aj] 115	65[aj] 115	27 105	2 3	7.6522 5.8803 [g][s]	1.7673
									1.3374[r]
Gear	R	1	2	3	4	5	6	7	8
Gear Ratio[b]	−3.7569 [s][g] ${\displaystyle -{\tfrac {3,956}{1,053}}}$	4.8889 ${\displaystyle {\tfrac {44}{9}}}$	3.1235[v] ${\displaystyle {\tfrac {253}{81}}}$	2.0334 ${\displaystyle {\tfrac {1,584}{779}}}$	1.6389 [r][v][w] ${\displaystyle {\tfrac {59}{36}}}$	1.2676[v] ${\displaystyle {\tfrac {49,572}{39,107}}}$	1.0000 ${\displaystyle {\tfrac {1}{1}}}$	0.8305 [v][w] ${\displaystyle {\tfrac {828}{997}}}$	0.6389 ${\displaystyle {\tfrac {23}{36}}}$
Step	0.7685[s]	1.0000	1.5652	1.5361	1.2407[r]	1.2929	1.2676	1.2041	1.2999
Δ Step[u]			1.0190[v]	1.2381	0.9596[v]	1.0200[v]	1.0527	0.9263[v]
Speed	-1.3013	1.0000	1.5652	2.4043	2.9831	3.8568	4.8889	5.8867	7.6522
Δ Speed	1.3013	1.0000	0.5652	0.8391	0.5787[w]	0.8738	1.0321	0.9979[w]	1.7654
Torque Ratio[c]	–3.5566 –3.4585	4.8111 4.7722	3.0513 3.0152	2.0132 2.0030	1.6181 1.6077	1.2556 1.2495	1.0000	0.8258 0.8234	0.6342 0.6318
Efficiency ${\displaystyle \eta _{n}}$[d]	0.9467 0.9206	0.9841 0.9761	0.9769 0.9654	0.9901 0.9851	0.9873 0.9810	0.9905 0.9857	1.0000	0.9943 0.9914	0.9927 0.9890
Actuated Shift Elements[al]
Brake A[am]	❶	❶	❶					❶	❶
Brake B[an]	❶	❶	❶	❶	❶	❶
Clutch C[ao]		❶		❶		❶	❶	❶
Clutch D[ap]	❶				❶	❶	❶	❶	❶
Clutch E[aq]			❶	❶	❶		❶		❶
Geometric Ratios: Speed Conversion
Gear Ratio[b] R & 1 & 2 Ordinary[ar] Elementary Noted[as]	${\displaystyle i_{R}={\frac {R_{2}(S_{3}S_{4}-R_{3}R_{4})}{S_{3}S_{4}(S_{2}+R_{2})}}}$			${\displaystyle i_{1}={\frac {S_{4}+R_{4}}{S_{4}}}}$			${\displaystyle i_{2}={\frac {R_{2}(S_{4}+R_{4})}{(S_{2}+R_{2})S_{4}}}}$
	${\displaystyle i_{R}={\tfrac {1-{\tfrac {R_{3}R_{4}}{S_{3}S_{4}}}}{1+{\tfrac {S_{2}}{R_{2}}}}}}$			${\displaystyle i_{1}=1+{\tfrac {R_{4}}{S_{4}}}}$			${\displaystyle i_{2}={\tfrac {1+{\tfrac {R_{4}}{S_{4}}}}{1+{\tfrac {S_{2}}{R_{2}}}}}}$
Gear Ratio[b] 3 & 4 Ordinary[ar] Elementary Noted[as]	${\displaystyle i_{3}={\frac {(S_{1}+R_{1})(S_{4}+R_{4})}{S_{4}R_{1}+S_{1}(S_{4}+R_{4})}}}$					${\displaystyle i_{4}=1+{\frac {S_{2}R_{1}}{S_{1}(S_{2}+R_{2})}}}$
	${\displaystyle i_{3}={\tfrac {1}{{\tfrac {1}{1+{\tfrac {R_{1}}{S_{1}}}}}+{\tfrac {1}{\left(1+{\tfrac {S_{1}}{R_{1}}}\right)\left(1+{\tfrac {R_{4}}{S_{4}}}\right)}}}}}$					${\displaystyle i_{4}=1+{\tfrac {\tfrac {R_{1}}{S_{1}}}{1+{\tfrac {R_{2}}{S_{2}}}}}}$
Gear Ratio[b] 5 Ordinary[ar] Elementary Noted[as]	${\displaystyle i_{5}={\frac {S_{1}R_{2}R_{4}(S_{3}+R_{3})+S_{2}S_{3}(S_{1}+R_{1})(S_{4}+R_{4})}{S_{1}R_{4}(S_{3}(S_{2}+R_{2})+R_{2}R_{3})+S_{2}S_{3}S_{4}(S_{1}+R_{1})}}}$
	${\displaystyle i_{5}={\tfrac {1}{{\tfrac {1}{{\tfrac {\left(1+{\tfrac {R_{1}}{S_{1}}}\right)\left(1+{\tfrac {S_{4}}{R_{4}}}\right)}{1+{\tfrac {R_{2}}{S_{2}}}\left(1+{\tfrac {R_{3}}{S_{3}}}\right)}}+{\tfrac {1}{{\tfrac {1}{1+{\tfrac {S_{3}}{R_{3}}}}}+{\tfrac {1+{\tfrac {S_{2}}{R_{2}}}}{1+{\tfrac {R_{3}}{S_{3}}}}}}}}}+{\tfrac {1}{1+{\tfrac {R_{4}}{S_{4}}}+{\tfrac {{\tfrac {R_{2}R_{4}}{S_{2}S_{4}}}\left(1+{\tfrac {R_{3}}{S_{3}}}\right)}{1+{\tfrac {R_{1}}{S_{1}}}}}}}}}}$
Gear Ratio[b] 6 – 8 Ordinary[ar] Elementary Noted[as]	${\displaystyle i_{6}={\frac {1}{1}}}$		${\displaystyle i_{7}={\frac {R_{2}(S_{3}+R_{3})}{R_{2}(S_{3}+R_{3})+S_{2}S_{3}}}}$				${\displaystyle i_{8}={\frac {R_{2}}{S_{2}+R_{2}}}}$
			${\displaystyle i_{7}={\tfrac {1}{1+{\tfrac {\tfrac {S_{2}}{R_{2}}}{1+{\tfrac {R_{3}}{S_{3}}}}}}}}$				${\displaystyle i_{8}={\tfrac {1}{1+{\tfrac {S_{2}}{R_{2}}}}}}$
Kinetic Ratios: Torque Conversion
Torque Ratio[c] R & 1 & 2	${\displaystyle \mu _{R}={\tfrac {1-{\tfrac {R_{3}R_{4}}{S_{3}S_{4}}}{\eta _{0}}^{2}}{1+{\tfrac {S_{2}}{R_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}}}$			${\displaystyle \mu _{1}=1+{\tfrac {R_{4}}{S_{4}}}{\eta _{0}}}$			${\displaystyle \mu _{2}={\tfrac {1+{\tfrac {R_{4}}{S_{4}}}\eta _{0}}{1+{\tfrac {S_{2}}{R_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}}}$
Torque Ratio[c] 3 & 4	${\displaystyle \mu _{3}={\tfrac {1}{{\tfrac {1}{1+{\tfrac {R_{1}}{S_{1}}}{\eta _{0}}^{\tfrac {1}{2}}}}+{\tfrac {1}{\left(1+{\tfrac {S_{1}}{R_{1}}}{\eta _{0}}^{\tfrac {1}{2}}\right)\left(1+{\tfrac {R_{4}}{S_{4}}}\eta _{0}\right)}}}}}$					${\displaystyle \mu _{4}=1+{\tfrac {{\tfrac {R_{1}}{S_{1}}}\eta _{0}}{1+{\tfrac {R_{2}}{S_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}}}$
Torque Ratio[c] 5	${\displaystyle \mu _{5}={\tfrac {1}{{\tfrac {1}{{\tfrac {\left(1+{\tfrac {R_{1}}{S_{1}}}{\eta _{0}}^{\tfrac {1}{2}}\right)\left(1+{\tfrac {S_{4}}{R_{4}}}{\eta _{0}}^{\tfrac {1}{3}}\right)}{1+{\tfrac {R_{2}}{S_{2}}}\cdot {\tfrac {1}{{\eta _{0}}^{\tfrac {1}{3}}}}\left(1+{\tfrac {R_{3}}{S_{3}}}\cdot {\tfrac {1}{{\eta _{0}}^{\tfrac {1}{4}}}}\right)}}+{\tfrac {1}{{\tfrac {1}{1+{\tfrac {S_{3}}{R_{3}}}{\eta _{0}}^{\tfrac {1}{4}}}}+{\tfrac {1+{\tfrac {S_{2}}{R_{2}}}\cdot {\tfrac {1}{{\eta _{0}}^{\tfrac {1}{3}}}}}{1+{\tfrac {R_{3}}{S_{3}}}{\eta _{0}}^{\tfrac {1}{4}}}}}}}}+{\tfrac {1}{1+{\tfrac {R_{4}}{S_{4}}}{\eta _{0}}^{\tfrac {1}{3}}+{\tfrac {{\tfrac {R_{2}R_{4}}{S_{2}S_{4}}}{\eta _{0}}^{\tfrac {2}{3}}\left(1+{\tfrac {R_{3}}{S_{3}}}{\eta _{0}}^{\tfrac {1}{4}}\right)}{1+{\tfrac {R_{1}}{S_{1}}}\cdot {\tfrac {1}{{\eta _{0}}^{\tfrac {1}{2}}}}}}}}}}}$
Torque Ratio[c] 6 – 8	${\displaystyle \mu _{6}={\tfrac {1}{1}}}$		${\displaystyle \mu _{7}={\tfrac {1}{1+{\tfrac {{\tfrac {S_{2}}{R_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}{1+{\tfrac {R_{3}}{S_{3}}}\eta _{0}}}}}}$				${\displaystyle \mu _{8}={\tfrac {1}{1+{\tfrac {S_{2}}{R_{2}}}\cdot {\tfrac {1}{\eta _{0}}}}}}$
^ 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 ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac 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 ${\displaystyle i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}}$ ^ a b c d e f g h i j k l m n o p q r s t u v w x y z 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 ${\displaystyle 0\leq \eta _{n;\eta _{0}}\leq 1}$ ^ a b c d e f g h i j k l m n o p q r s t u v 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) ^ Layout Input and output are on opposite sides Planetary gearset 1 is on the input (turbine) side Input (turbine) shafts are C2 and, if actuated, R3 and S4 Output shaft is C4 ^ 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 ^ a b c d e f g h i j k l m n o p q r s t u v w x y z 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 ^ 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 ${\displaystyle \left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}}$ 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 ^ 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 ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an 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 3) is always larger and the upper half of the gear steps (between the large gears; rounded up, here the last 4) 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) ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al 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 ^ 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) ^ a b c d e f g h i j k l From large to small gears (from right to left) ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh bi bj bk bl bm bn bo bp bq br bs bt bu bv bw bx by bz ca cb cc cd ce cf cg ch ci cj ck cl cm cn co cp cq cr cs 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) ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw 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) ^ w/o generation designation ^ The new BMW M760 Li xDrive · BMW Media Information Germany · 02/2016 · P. 23 · German: Der neue BMW M760 Li xDrive · BMW Medieninformation Deutschland · BMW Media Information Germany · 02/2016 · S. 23 · and The new BMW M760 Li xDrive · Technical Specifications · BMW Media Information Austria · 01/2017 · P. 2 · German: Der neue BMW M760 Li xDrive · Technische Daten · BMW Medieninformation Österreich · 01/2017 · S. 2 · 800 N⋅m (590 lb⋅ft)[20][7] ^ narrow total ratio span · preferebly for petrol engines, sports cars, and high performance engines · Alpina B3 Saloon AWD · Technical Data · 730 N⋅m (538 lb⋅ft)[21][7] ^ Technical specifications · The new BMW 3 Series Sedan · BMW Media Information · 03/2019 · p. 2: BMW 320i Sedan · 300 N⋅m (221 lb⋅ft)[22][7] ^ loc. cit. · p. 10: BMW M340i xDrive Sedan · 500 N⋅m (369 lb⋅ft)[22][7] ^ wide total ratio span · preferebly for Diesel engines, offroad cars, and low performance engines · loc. cit. · p. 18: BMW 330d Sedan · 580 N⋅m (428 lb⋅ft)[22][7] and Alpina D3 S Saloon AWD · Technical Data · 730 N⋅m (538 lb⋅ft)[23] ^ narrow total ratio span · preferebly for petrol engines, sports cars, and high performance engines · The first-ever BMW XM · Market launch September 2022[24][25] The all-new BMW M5 · Market launch June 2024[26][27] ^ wide total ratio span · preferebly for Diesel engines, offroad cars, and low performance engines · Progress and efficiency with added variety: additional drive system variants and innovations for the new BMW 7 Series · Market launch 2022/2023[28][29] Alpina XB7 AWD · Technical Data[30] ^ w/o hydraulic torque converter · narrow total ratio span of 4.2[9] ^ based on the same gearset concept as the 8HP transmissions[31][32] ^ Automatic Powershift Transmission for Trucks[33] ^ a b higher torque on demand[10] ^ a b c d e 65/115 or 52/92[10][34] ^ Automatic Powershift Transmission for Special vehicles[34][35] ^ Permanently coupled elements S1 and S2 C1 and R4 R2 and S3 R3 and S4 ^ Blocks S1 and S2 ^ Blocks R1 ^ Couples R3 and S4 with the input (turbine) ^ Couples C3 with C4 ^ Couples R2 and S3 with R3 and S4 ^ a b c d Ordinary Noted For direct determination of the gear ratio ^ a b c d 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