In-Depth Analysis [ b] [ c] [ d] Planetary Gearset: [ e] Teeth Count Nomi- [ f] [ g] Cen- [ h] Simpson Avg. [ i] Model Version S1 [ j] 1 [ k] S2 [ l] 2 [ m] Brakes Ratio Gear [ n] Gear R 1 2 3 Gear [ b] i R {\displaystyle {i_{R}}} [ b] i 1 {\displaystyle {i_{1}}} [ b] i 2 {\displaystyle {i_{2}}} [ b] i 3 {\displaystyle {i_{3}}} [ b] Step [ n] − i R i 1 {\displaystyle -{\frac {i_{R}}{i_{1}}}} [ o] i 1 i 1 {\displaystyle {\frac {i_{1}}{i_{1}}}} i 1 i 2 {\displaystyle {\frac {i_{1}}{i_{2}}}} [ p] i 2 i 3 {\displaystyle {\frac {i_{2}}{i_{3}}}} Δ Step [ q] [ r] i 1 i 2 : i 2 i 3 {\displaystyle {\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}} Shaft i 1 i R {\displaystyle {\frac {i_{1}}{i_{R}}}} i 1 i 1 {\displaystyle {\frac {i_{1}}{i_{1}}}} i 1 i 2 {\displaystyle {\frac {i_{1}}{i_{2}}}} i 1 i 3 {\displaystyle {\frac {i_{1}}{i_{3}}}} Δ Shaft [ s] 0 − i 1 i R {\displaystyle 0-{\tfrac {i_{1}}{i_{R}}}} i 1 i 1 − 0 {\displaystyle {\tfrac {i_{1}}{i_{1}}}-0} i 1 i 2 − i 1 i 1 {\displaystyle {\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}} i 1 i 3 − i 1 i 2 {\displaystyle {\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}} Torque [ c] μ R {\displaystyle \mu _{R}} [ c] μ 1 {\displaystyle \mu _{1}} [ c] μ 2 {\displaystyle \mu _{2}} [ c] μ 3 {\displaystyle \mu _{3}} [ c] Efficiencyη n {\displaystyle \eta _{n}} [ d] μ R i R {\displaystyle {\frac {\mu _{R}}{i_{R}}}} [ d] μ 1 i 1 {\displaystyle {\frac {\mu _{1}}{i_{1}}}} [ d] μ 2 i 2 {\displaystyle {\frac {\mu _{2}}{i_{2}}}} [ d] μ 3 i 3 {\displaystyle {\frac {\mu _{3}}{i_{3}}}} [ d] 3HP 22 320 N⋅m (236 lb⋅ft ) 35 35 3 2.4795 2.0857 [ g] [ o] 1.5746 1.5746 [ n] Gear R 1 2 3 Gear [ b] −2.0857 [ o] [ g] − 2 1 {\displaystyle -{\tfrac {2}{1}}} 2.4795 181 73 {\displaystyle {\tfrac {181}{73}}} 1.4795 [ p] 108 73 {\displaystyle {\tfrac {108}{73}}} 1.0000 1 1 {\displaystyle {\tfrac {1}{1}}} Step 0.8412 [ o] 1.0000 1.6759 [ p] 1.4795 Δ Step [ q] 1.1328 Speed -1.1888 1.0000 1.6759 2.4795 Δ Speed 1.1888 1.0000 0.6759 0.8035 Torque [ c] –2.0440 2.4303 1.4699 1.0000 Efficiencyη n {\displaystyle \eta _{n}} [ d] 0.9800 0.9802 0.9935 1.0000 3HP 22 Small Engines 35 41 3 2.7331 2.0857 [ g] [ o] 1.6532 1.6532 [ n] Gear R 1 2 3 Gear [ b] −2.0857 [ o] [ g] − 73 35 {\displaystyle -{\tfrac {73}{35}}} 2.7331 6 , 983 2 , 555 {\displaystyle {\tfrac {6,983}{2,555}}} 1.5616 [ p] 114 73 {\displaystyle {\tfrac {114}{73}}} 1.0000 1 1 {\displaystyle {\tfrac {1}{1}}} Step 0.7631 [ o] 1.0000 1.7501 [ p] 1.5616 Δ Step [ q] 1.1207 Speed -1.3103 1.0000 1.7501 2.7331 Δ Speed 1.3103 1.0000 0.7501 0.9829 Torque [ c] –2.0440 2.6755 1.5504 1.0000 Efficiencyη n {\displaystyle \eta _{n}} [ d] 0.9800 0.9789 0.9928 1.0000 3HP 22 Porsche 944 28 32 3 2.7143 2.4286 [ g] [ o] 1.6475 1.6475 [ n] Gear R 1 2 3 Gear [ b] −2.4286 [ o] [ g] − 17 7 {\displaystyle -{\tfrac {17}{7}}} 2.7143 19 7 {\displaystyle {\tfrac {19}{7}}} 1.5000 [ p] 3 2 {\displaystyle {\tfrac {3}{2}}} 1.0000 1 1 {\displaystyle {\tfrac {1}{1}}} Step 0.8947 [ o] 1.0000 1.8095 [ p] 1.5000 Δ Step [ q] 1.2063 Speed -1.1176 1.0000 1.8095 2.7143 Δ Speed 1.1176 1.0000 0.8095 0.9048 Torque [ c] –2.3800 2.6562 1.4900 1.0000 Efficiencyη n {\displaystyle \eta _{n}} [ d] 0.9800 0.9786 0.9933 1.0000 Actuated Shift Elements Brake A [ t] ❶ Brake B [ u] ❶ ❶ Brake C [ v] ❶ ❶ Clutch D [ w] ❶ ❶ ❶ Clutch E [ x] ❶ ❶ Geometric Ratios Gear [ b] [ y] [ z] i R = − R 1 S 1 {\displaystyle i_{R}=-{\frac {R_{1}}{S_{1}}}} i 2 = S 2 + R 2 R 2 {\displaystyle i_{2}={\frac {S_{2}+R_{2}}{R_{2}}}} i R = − R 1 S 1 {\displaystyle i_{R}=-{\tfrac {R_{1}}{S_{1}}}} i 2 = 1 + S 2 R 2 {\displaystyle i_{2}=1+{\tfrac {S_{2}}{R_{2}}}} Gear [ b] [ y] [ z] i 1 = S 1 ( S 2 + R 2 ) + R 1 S 2 S 1 R 2 {\displaystyle i_{1}={\frac {S_{1}(S_{2}+R_{2})+R_{1}S_{2}}{S_{1}R_{2}}}} i 3 = 1 1 {\displaystyle i_{3}={\frac {1}{1}}} i 1 = 1 + S 2 R 2 ( 1 + R 1 S 1 ) {\displaystyle i_{1}=1+{\tfrac {S_{2}}{R_{2}}}\left(1+{\tfrac {R_{1}}{S_{1}}}\right)} Kinetic Ratios: ´Torque Conversion Torque [ c] μ R = − R 1 S 1 η 0 {\displaystyle \mu _{R}=-{\tfrac {R_{1}}{S_{1}}}\eta _{0}} μ 2 = 1 + S 2 R 2 η 0 {\displaystyle \mu _{2}=1+{\tfrac {S_{2}}{R_{2}}}\eta _{0}} Torque [ c] & 3 μ 1 = 1 + S 2 R 2 η 0 ( 1 + R 1 S 1 η 0 ) {\displaystyle \mu _{1}=1+{\tfrac {S_{2}}{R_{2}}}\eta _{0}\left(1+{\tfrac {R_{1}}{S_{1}}}\eta _{0}\right)} μ 3 = 1 1 {\displaystyle \mu _{3}={\tfrac {1}{1}}} ↑ Revised 14 January 2026Nomenclature S n = {\displaystyle S_{n}=} R n = {\displaystyle R_{n}=} C n = {\displaystyle \color {gray}{C_{n}=}} carrier or planetary gear carrier (not needed) s n = {\displaystyle s_{n}=} r n = {\displaystyle r_{n}=} c n = {\displaystyle c_{n}=} n = {\displaystyle n=} i n = {\displaystyle i_{n}=} ω 1 ; n = ω t = {\displaystyle \omega _{1;n}=\omega _{t}=} ω 2 ; n = {\displaystyle \omega _{2;n}=} T 1 ; n = T t = {\displaystyle T_{1;n}=T_{t}=} T 2 ; n = {\displaystyle T_{2;n}=} μ n = {\displaystyle \mu _{n}=} η n = {\displaystyle \eta _{n}=} i 0 = {\displaystyle i_{0}=} η 0 = {\displaystyle \eta _{0}=} 1 2 3 4 5 6 7 8 9 10 11 Gear Ratio (Transmission Ratio) i n {\displaystyle i_{n}} — Speed Conversion — The gear ratio i n {\displaystyle i_{n}} is the ratio of input shaft speed ω 1 ; n {\displaystyle \omega _{1;n}} to output shaft speed ω 2 ; n {\displaystyle \omega _{2;n}} and therefore corresponds to the reciprocal of the shaft speeds i n = 1 ω 2 ; n ω 1 ; n = ω 1 ; n ω 2 ; n = ω t ω 2 ; n {\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}}}} 1 2 3 4 5 6 7 8 9 10 11 Torque Ratio (Torque Conversion Ratio) μ n {\displaystyle \mu _{n}} — Torque Conversion — The torque ratio μ n {\displaystyle \mu _{n}} is the ratio of output torque T 2 ; n {\displaystyle T_{2;n}} to input torque T 1 ; n {\displaystyle T_{1;n}} minus efficiency losses and therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too μ n = i n η n ; η 0 = ω 1 ; n η n ; η 0 ω 2 ; n = T 2 ; n η n ; η 0 T 1 ; n {\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 η n ; η 0 {\displaystyle \eta _{n;\eta _{0}}} 0 ≤ η n ; η 0 ≤ 1 {\displaystyle 0\leq \eta _{n;\eta _{0}}\leq 1} 1 2 3 4 5 6 7 8 9 Efficiency The efficiency η n {\displaystyle \eta _{n}} from the torque ratio in relation to the gear ratio (transmission ratio) η n = μ n i n {\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 i 0 {\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 η 0 {\displaystyle \eta _{0}} stationary ratio i 0 {\displaystyle i_{0}} of η 0 = 0.9800 {\displaystyle \eta _{0}=0.9800} and η 0 = 0.9700 {\displaystyle \eta _{0}=0.9700} for both interventions together The corresponding efficiency for single-meshing gear pairs is η 0 1 2 {\displaystyle {\eta _{0}}^{\tfrac {1}{2}}} at 0.9800 1 2 = 0.98995 {\displaystyle 0.9800^{\tfrac {1}{2}}=0.98995} and 0.9700 1 2 = 0.98489 {\displaystyle 0.9700^{\tfrac {1}{2}}=0.98489} ↑ Layout Input and output are on opposite sides Planetary gearset 1 is on the input (turbine) side Input (turbine) shaft is, if actuated, S1 or R2 Output shaft is R1 ↑ Total Ratio Span (Total Gear/Transmission Ratio) Nominal ω 2 ; n ω 2 ; 1 = ω 2 ; n ω 2 ; 1 ω 2 ; n ω 2 ; 1 ω 2 ; 1 ω 2 ; n = 1 ω 2 ; 1 1 ω 2 ; n = ω t ω 2 ; 1 ω t ω 2 ; n = i 1 i n {\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 1 2 3 4 5 6 7 Total Ratio Span (Total Gear Ratio/Total Transmission Ratio) Effective ω 2 ; n m a x ( ω 2 ; 1 ; | ω 2 ; R | ) = m i n ( i 1 ; | i R | ) i n {\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 is usually longer than 1st gear the effective span is therefore of central importance for describing the suitability of a transmission because in these cases, the nominal spread conveys a misleading picture which is only unproblematic for vehicles with high specific power Market participants Manufacturers naturally have no interest in specifying the effective span Users have not yet formulated the practical benefits that the effective span has for them The effective span has not yet played a role in research and teaching Contrary to its significance the effective span has therefore not yet been able to establish itself either in theory or in practice. End of digression ↑ Ratio Span's Center ( i 1 i n ) 1 2 {\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 ( ω 2 ; n ω 2 ; 1 ) 1 n − 1 = ( i 1 i n ) 1 n − 1 {\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 n − 1 {\displaystyle n-1} n {\displaystyle n} with decreasing step width the gears connect better to each other shifting comfort increases ↑ Sun 1: sun gear of gearset 1: inner Ravigneaux gearset ↑ Ring 1: ring gear of gearset 1: inner Ravigneaux gearset ↑ Sun 2: sun gear of gearset 2: outer Ravigneaux gearset ↑ Ring 2: ring gear of gearset 2: outer Ravigneaux gearset 1 2 3 4 5 Standard 50:50— 50 % Is Above And 50 % Is Below The Average Gear Step — With steadily decreasing gear steps (yellow highlighted line Step ) and a particularly large step from 1st to 2nd gear the lower half of the gear steps (between the small gears; rounded down, here the first 1) is always larger and the upper half of the gear steps (between the large gears; rounded up, here the last 1) is always smaller than the average gear step (cell highlighted yellow two rows above on the far right)lower half: smaller gear steps are a waste of possible ratios (red bold) upper half: larger gear steps are unsatisfactory (red bold) 1 2 3 4 5 6 7 8 9 10 Standard R:1— Reverse And 1st Gear Have The Same Ratio — The ideal reverse gear has the same transmission ratio as 1st gear no impairment when maneuvering especially when towing a trailer a torque converter can only partially compensate for this deficiency Plus 11.11 % minus 10 % compared to 1st gear is good Plus 25 % minus 20 % is acceptable (red) Above this is unsatisfactory (bold) 1 2 3 4 5 6 7 Standard 1:2— Gear Step 1st To 2nd Gear As Small As Possible — With continuously decreasing gear steps (yellow marked line Step ) the largest gear step is the one from 1st to 2nd gear, which for a good speed connection and a smooth gear shift must be as small as possible A gear ratio of up to 1.6667 : 1 (5 : 3) is good Up to 1.7500 : 1 (7 : 4) is acceptable (red) Above is unsatisfactory (bold) 1 2 3 4 From large to small gears (from right to left) ↑ Standard STEP— From Large To Small Gears: Steady And Progressive Increase In Gear Steps — Gear steps should increase: Δ Step (first green highlighted line Δ Step ) is always greater than 1As progressive as possible: Δ Step is always greater than the previous step Not progressively increasing is acceptable (red) Not increasing is unsatisfactory (bold) ↑ Standard SPEED— From Small To Large Gears: Steady Increase In Shaft Speed Difference — Shaft speed differences should increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed ) is always greater than the previous one 1 difference smaller than the previous one is acceptable (red) 2 consecutive ones are a waste of possible ratios (bold) ↑ Blocks S1 ↑ Supports link with freewheel · blocks S1 in one direction ↑ Blocks C1 ↑ Couples S1 with the input (turbine) ↑ Couples R2 with the input (turbine) 1 2 Ordinary Noted For direct determination of the gear ratio 1 2 Elementary Noted Alternative representation for determining the transmission ratio Contains only operands With simple fractions of both central gears of a planetary gearset Or with the value 1 As a basis For reliable And traceable Determination of the torque conversion ratio and efficiency 
