Aja viide. Aja lugu.

The 3HP is a 3-speed Automatic transmission family with a hydrodynamic Torque converter with hydraulic control for passenger cars from ZF Friedrichshafen AG. In selector level position "P", the output is locked mechanically. The Ravigneaux planetary gearset types were first introduced in 1963 and produced through the mid seventies. The Simpson planetary gearset types were launched in 1973 and produced through 1990. Both were used in different versions in a large number of cars.

Gear Ratios^[a]
Gear Model	R	1	2	3	Total Span	Span Center	Avg. Step	Compo- nents

3HP 12 Small Engines	−2.000	2.560	1.520	1.000	2.560	1.600	1.600	2 Gearsets 3 Brakes 2 Clutches
3HP 12 Big Engines	−2.000	2.286	1.429	1.000	2.286	1.512	1.512	2 Gearsets 3 Brakes 2 Clutches

3HP 22 Big Engines	−2.086	2.479	1.479	1.000	2.479	1.575	1.575	2 Gearsets 3 Brakes 2 Clutches
3HP 22 Small Engines	−2.086	2.733	1.562	1.000	2.733	1.653	1.653
3HP 22 Porsche 944	−2.429	2.714	1.500	1.000	2.714	1.648	1.648

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

1963: 3HP 12 · Ravigneaux Planetary Gearset Types

Introduction

The 3HP 12 was produced through the mid-seventies and has been used in a variety of cars. There are versions for longitudinal and transverse engines.

Gear Ratios
With Assessment		Planetary Gearset: Teeth^[a] Ravigneaux		Count	Total^[b] Center^[c]	Avg.^[d]

Model Type	Version First Delivery	S₁^[e] R₁^[f]	S₂^[g] R₂^[h]	Brakes Clutches	Ratio Span	Gear Step^[i]
Gear Ratio		R ${i_{R}}$		1 ${i_{1}}$	2 ${i_{2}}$	3 ${i_{3}}$
Step^[i]		$-{\tfrac {i_{R}}{i_{1}}}$ ^[j]		${\tfrac {i_{1}}{i_{1}}}$	${\tfrac {i_{1}}{i_{2}}}$ ^[k]	${\tfrac {i_{2}}{i_{3}}}$
Δ Step^[l]^[m]					${\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}$
Shaft Speed		${\tfrac {i_{1}}{i_{R}}}$		${\tfrac {i_{1}}{i_{1}}}$	${\tfrac {i_{1}}{i_{2}}}$	${\tfrac {i_{1}}{i_{3}}}$
Δ Shaft Speed^[n]		$0-{\tfrac {i_{1}}{i_{R}}}$		${\tfrac {i_{1}}{i_{1}}}-0$	${\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}$	${\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}$

3HP 12	160 N⋅m (118 lb⋅ft) 1963	25 32	32 64	3 2	2.5600 1.6000	1.6000^[i]
Gear Ratio		−2.0000^[j] $-{\tfrac {2}{1}}$		2.5600 ${\tfrac {64}{25}}$	1.5200^[k] ${\tfrac {38}{25}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.7825^[j]		1.0000	1.6842^[k]	1.5200
Δ Step^[l]					1.1080
Speed		-1.2800		1.0000	1.6842	2.5600
Δ Speed		1.2800		1.0000	0.6842	0.8758

3HP 12	Big Engines 1963	28 32	32 64	3 2	2.2857 1.5119	1.5119^[i]
Gear Ratio		−2.0000^[j] $-{\tfrac {2}{1}}$		2.2857 ${\tfrac {16}{7}}$	1.4286 ${\tfrac {10}{7}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.8750^[j]		1.0000	1.6000	1.4286
Δ Step^[l]					1.1280
Speed		-1.1429		1.0000	1.6000	2.2857
Δ Speed		1.1429		1.0000	0.6000	0.6842

Ratio		$-{\tfrac {R_{2}}{S_{2}}}$		${\tfrac {R_{1}R_{2}}{S_{1}S_{2}}}$	${\tfrac {R_{2}(S_{1}+R_{1})}{S_{1}(S_{2}+R_{2})}}$	${\tfrac {1}{1}}$
Algebra And Actuated Shift Elements
Brake A^[o]					❶
Brake B^[p]					❶
Brake C^[q]		❶		❶
Clutch D^[r]				❶	❶	❶
Clutch E^[s]		❶				❶

^ Layout Input and output are on opposite sides Planetary gearset 2 (the outer Ravigneaux gearset) is on the input (turbine) side Input shafts is, if actuated S₁ or S₂ Output shaft is R₂ (the ring gear of the outer Ravigneaux gearset ^ Total Ratio Span (Total Ratio Spread · Total Gear Ratio) ${\tfrac {i_{n}}{i_{1}}}$ 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 ^ Ratio Span's Center $(i_{n}i_{1})^{\tfrac {1}{2}}$ 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 $({\tfrac {i_{n}}{i_{1}}})^{\tfrac {1}{n-1}}$ 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 ^ ^a ^b ^c ^d 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) ^ ^a ^b ^c ^d ^e 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) ^ ^a ^b ^c 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 From large to small gears (from right to left) ^ Standard STEP — From Large To Small Gears: Steady And Progressive Increase In Gear Steps — Gear steps should increase: Δ Step (first green highlighted line Δ Step) is always greater than 1 As progressive as possible: Δ Step is always greater than the previous step Not progressively increasing is acceptable (red) Not increasing is unsatisfactory (bold) ^ Standard SPEED — From Small To Large Gears: Steady Increase In Shaft Speed Difference — Shaft speed differences should increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one 1 difference smaller than the previous one is acceptable (red) 2 consecutive ones are a waste of possible ratios (bold) ^ Blocks R₁ (ring gear of the inner Ravigneaux gearset) and S₂ (sun gear of the outer Ravigneaux gearset) ^ Support link with freewheel · blocks R₁ (ring gear of the inner Ravigneaux gearset) and S₂ (sun gear of the outer Ravigneaux gearset) in one direction ^ Blocks C₁ and C₂ (the common Ravigneaux carrier 1 + 2) ^ Couples S₁ (sun gear of the inner Ravigneaux gearset) with the turbine ^ Couples S₂ (sun gear of the outer Ravigneaux gearset) with the turbine

1973: 3HP 22 · Simpson Planetary Gearset Types

Introduction

The all new 3HP 22 was introduced in 1973 and was produced through 1990 and has been used in a variety of cars from Alfa Romeo, BMW,^[1] Citroën, Peugeot, and Fiat.^[2]

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

Gear Ratios
With Assessment		Planetary Gearset: Teeth^[a] Simpson		Count	Total^[b] Center^[c]	Avg.^[d]

Model Type	Version First Delivery	S₁^[e] R₁^[f]	S₂^[g] R₂^[h]	Brakes Clutches	Ratio Span	Gear Step^[i]
Gear Ratio		R ${i_{R}}$		1 ${i_{1}}$	2 ${i_{2}}$	3 ${i_{3}}$
Step^[i]		$-{\tfrac {i_{R}}{i_{1}}}$ ^[j]		${\tfrac {i_{1}}{i_{1}}}$	${\tfrac {i_{1}}{i_{2}}}$ ^[k]	${\tfrac {i_{2}}{i_{3}}}$
Δ Step^[l]^[m]					${\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}$
Shaft Speed		${\tfrac {i_{1}}{i_{R}}}$		${\tfrac {i_{1}}{i_{1}}}$	${\tfrac {i_{1}}{i_{2}}}$	${\tfrac {i_{1}}{i_{3}}}$
Δ Shaft Speed^[n]		$0-{\tfrac {i_{1}}{i_{R}}}$		${\tfrac {i_{1}}{i_{1}}}-0$	${\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}$	${\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}$

3HP 22	320 N⋅m (236 lb⋅ft) 1963	35 73	35 73	3 2	2.4795 1.5746	1.5746^[i]
Gear Ratio		−2.0857^[j] $-{\tfrac {2}{1}}$		2.4795 ${\tfrac {181}{73}}$	1.4795^[k] ${\tfrac {108}{73}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.8412^[j]		1.0000	1.6759^[k]	1.4795
Δ Step^[l]					1.1328
Speed		-1.1888		1.0000	1.6759	2.4795
Δ Speed		1.1888		1.0000	0.6759	0.8035

3HP 22	Small Engines 1973	35 73	41 73	3 2	2.7331 1.6532	1.6532^[i]
Gear Ratio		−2.0857^[j] $-{\tfrac {73}{35}}$		2.7331 ${\tfrac {6983}{2555}}$	1.5616^[k] ${\tfrac {114}{73}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.7631^[j]		1.0000	1.7501^[k]	1.5616
Δ Step^[l]					1.1207
Speed		-1.3103		1.0000	1.7501	2.7331
Δ Speed		1.3103		1.0000	0.7501	0.9829

3HP 22	Porsche 944 1981	28 68	32 64	3 2	2.7143 1.6475	1.6475^[i]
Gear Ratio		−2.4286^[j] $-{\tfrac {17}{7}}$		2.7143 ${\tfrac {19}{7}}$	1.5000^[k] ${\tfrac {3}{2}}$	1.0000 ${\tfrac {1}{1}}$
Step		0.8947^[j]		1.0000	1.8095^[k]	1.5000
Δ Step^[l]					1.2063
Speed		-1.1176		1.0000	1.8095	2.7143
Δ Speed		1.1176		1.0000	0.8095	0.9048

Ratio		$-{\tfrac {R_{1}}{S_{1}}}$	${\tfrac {S_{1}(S_{2}+R_{2})+R_{1}S_{2}}{S_{1}R_{2}}}$		${\tfrac {S_{2}+R_{2}}{R_{2}}}$	${\tfrac {1}{1}}$
Algebra And Actuated Shift Elements
Brake A^[o]					❶
Brake B^[p]					❶	❶
Brake C^[q]		❶		❶
Clutch D^[r]				❶	❶	❶
Clutch E^[s]		❶				❶

^ Layout Input and output are on opposite sides Planetary gearset 1 is on the input (turbine) side Input shafts is, if actuated, S₁ or R₂ Output shaft is R₁ ^ Total Ratio Span (Total Ratio Spread · Total Gear Ratio) ${\tfrac {i_{n}}{i_{1}}}$ 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 ^ Ratio Span's Center $(i_{n}i_{1})^{\tfrac {1}{2}}$ 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 $({\tfrac {i_{n}}{i_{1}}})^{\tfrac {1}{n-1}}$ 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 ^ ^a ^b ^c ^d ^e 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) ^ ^a ^b ^c ^d ^e ^f ^g 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) ^ ^a ^b ^c ^d ^e ^f ^g 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 From large to small gears (from right to left) ^ Standard STEP — From Large To Small Gears: Steady And Progressive Increase In Gear Steps — Gear steps should increase: Δ Step (first green highlighted line Δ Step) is always greater than 1 As progressive as possible: Δ Step is always greater than the previous step Not progressively increasing is acceptable (red) Not increasing is unsatisfactory (bold) ^ Standard SPEED — From Small To Large Gears: Steady Increase In Shaft Speed Difference — Shaft speed differences should increase: Δ Shaft Speed (second line marked in green Δ (Shaft) Speed) is always greater than the previous one 1 difference smaller than the previous one is acceptable (red) 2 consecutive ones are a waste of possible ratios (bold) ^ Blocks S₁ ^ Support link with freewheel · blocks S₁ in one direction ^ Blocks C₁ (the planetary gear carrier 1) ^ Couples S₁ with the turbine ^ Couples R₂ with the turbine

References

^ "BMWE21.net". BMWe21.net. Retrieved 24 November 2013.
^ "ZF North America application chart (automatic)". ZF.com. Retrieved 22 November 2013.

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

[2] Layout
Input and output are on opposite sides

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

Input shafts is, if actuated S₁ or S₂

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

[3] Input and output are on opposite sides

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

[5] Input shafts is, if actuated S₁ or S₂

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

[3] Total Ratio Span (Total Ratio Spread · Total Gear Ratio)
${\tfrac {i_{n}}{i_{1}}}$

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

[8] ${\tfrac {i_{n}}{i_{1}}}$

[9] 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

[10] wnspeeding when driving outside the city limits

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

or when towing a trailer

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

[13] r when towing a trailer

[4] Ratio Span's Center
$(i_{n}i_{1})^{\tfrac {1}{2}}$

The center indicates the speed level of the transmission

Together with the final drive ratio

it gives the shaft speed level of the vehicle

[15] $(i_{n}i_{1})^{\tfrac {1}{2}}$

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

[17] Together with the final drive ratio

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

[5] Average Gear Step
$({\tfrac {i_{n}}{i_{1}}})^{\tfrac {1}{n-1}}$

With decreasing step width
the gears connect better to each other

shifting comfort increases

[20] $({\tfrac {i_{n}}{i_{1}}})^{\tfrac {1}{n-1}}$

[21] With decreasing step width
the gears connect better to each other

shifting comfort increases

[22] the gears connect better to each other

[23] shifting comfort increases

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

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

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

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

[50:50-10] 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)

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

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

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

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

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

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

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

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

[R:1-11] 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)

[37] 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

[38] rment when maneuvering

[39] specially when towing a trailer

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

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

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

[43] Above this is unsatisfactory (bold)

[1:2-12] 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)

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

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

a smooth gear shift

[47] r a good speed connection and

[48] smooth gear shift

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

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

Above is unsatisfactory (bold)

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

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

[52] Above is unsatisfactory (bold)

[LS-13] From large to small gears (from right to left)

[step-14] 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)

[55] 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

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

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

[58] Not progressively increasing is acceptable (red)

[59] Not increasing is unsatisfactory (bold)

[speed-15] 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)

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

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

[63] 1 difference smaller than the previous one is acceptable (red)

[64] 2 consecutive ones are a waste of possible ratios (bold)

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

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

[18] Blocks C₁ and C₂ (the common Ravigneaux carrier 1 + 2)

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

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

[23] Layout
Input and output are on opposite sides

Planetary gearset 1 is on the input (turbine) side

Input shafts is, if actuated, S₁ or R₂

Output shaft is R₁

[71] Input and output are on opposite sides

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

[73] Input shafts is, if actuated, S₁ or R₂

[74] Output shaft is R₁

[24] Total Ratio Span (Total Ratio Spread · Total Gear Ratio)
${\tfrac {i_{n}}{i_{1}}}$

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

[76] ${\tfrac {i_{n}}{i_{1}}}$

[77] 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

[78] wnspeeding when driving outside the city limits

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

or when towing a trailer

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

[81] r when towing a trailer

[25] Ratio Span's Center
$(i_{n}i_{1})^{\tfrac {1}{2}}$

The center indicates the speed level of the transmission

Together with the final drive ratio

it gives the shaft speed level of the vehicle

[83] $(i_{n}i_{1})^{\tfrac {1}{2}}$

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

[85] Together with the final drive ratio

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

[26] Average Gear Step
$({\tfrac {i_{n}}{i_{1}}})^{\tfrac {1}{n-1}}$

With decreasing step width
the gears connect better to each other

shifting comfort increases

[88] $({\tfrac {i_{n}}{i_{1}}})^{\tfrac {1}{n-1}}$

[89] With decreasing step width
the gears connect better to each other

shifting comfort increases

[90] the gears connect better to each other

[91] shifting comfort increases

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

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

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

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

[50:50-31] 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)

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

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

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

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

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

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

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

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

[R:1-32] ^ ^a ^b ^c ^d ^e ^f ^g 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)

[105] 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

[106] rment when maneuvering

[107] specially when towing a trailer

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

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

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

[111] Above this is unsatisfactory (bold)

[1:2-33] ^ ^a ^b ^c ^d ^e ^f ^g 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)

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

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

a smooth gear shift

[115] r a good speed connection and

[116] smooth gear shift

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

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

Above is unsatisfactory (bold)

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

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

[120] Above is unsatisfactory (bold)

[LS-34] From large to small gears (from right to left)

[step-35] 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)

[123] 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

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

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

[126] Not progressively increasing is acceptable (red)

[127] Not increasing is unsatisfactory (bold)

[speed-36] 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)

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

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

[131] 1 difference smaller than the previous one is acceptable (red)

[132] 2 consecutive ones are a waste of possible ratios (bold)

[37] Blocks S₁

[38] Support link with freewheel · blocks S₁ in one direction

[39] Blocks C₁ (the planetary gear carrier 1)

[40] Couples S₁ with the turbine

[41] Couples R₂ with the turbine

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

[22] "ZF North America application chart (automatic)". ZF.com. Retrieved 22 November 2013.

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