# Calculating top speed in each gear given the gear ratios and

Hello,

Can you tell me if there is anyway of calculating the top speed in each gear of a vehicle given its horsepower and gear ratios?

Since Power = Force*Velocity

Velocity = Power/Force
Force = Drag Force + Rolling Resistance

--> Velocity = Power / (Drag Force + Rolling Resistance)

This does give me the top speed of the vehicle but it doesnt tell me what the top speed in each gear would be?

This is how I found the top speed in each gear before:

Prop Shaft speed = Engine RPM / Selected Gear Ratio

Wheel Speed = Prop shaft speed / Final Drive Ratio

Vehicle Speed = Wheel Speed * PI * Wheel Diameter

The problem with the above is that for overdrive gears it gives extremely inaccurate and high speeds.

Thanks

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mfb
Mentor
You need more data about the motor and the gear - internal friction, maximum rpm and so on. The power you need at the wheels depends on the speed only, but the power the car can deliver depends on rpm and gear.

You need more data about the motor and the gear - internal friction, maximum rpm and so on. The power you need at the wheels depends on the speed only, but the power the car can deliver depends on rpm and gear.
Lets say the losses from the engine to the wheels is 15% (Including internal friction etc), the maximum engine speed is 9000 RPM. I already have the power at the wheels from a dyno test, I just need to theoretically determine the top speed in each gear.

mfb
Mentor
Assuming the engine can reach those 9000 rpm in each gear, you can calculate the corresponding velocity with the gear ratio and wheel diameter.

Assuming the engine can reach those 9000 rpm in each gear, you can calculate the corresponding velocity with the gear ratio and wheel diameter.
that is what I did before but it gives me unrealistically high values in overdrive gears with gear ratios less than 1. In those gears I need to factor in power somehow.

mfb
Mentor
Power will depend on rpm - for a proper calculation you'll need the corresponding curve. An easier estimate is to assume both are just limited by some fixed value, and to take the one that gives the lower limit on speed. This will still give an overestimate for the top speed.

Power will depend on rpm - for a proper calculation you'll need the corresponding curve. An easier estimate is to assume both are just limited by some fixed value, and to take the one that gives the lower limit on speed. This will still give an overestimate for the top speed.
I do have the power and engine speed curves from the dyno test. Do you mean assume that the top speed of the vehicle is limited by a fixed value? I need to basically model the car and give an estimate of the top speed before it goes on road test so I don't have any real time vehicle speed data.

mfb
Mentor
Do you mean assume that the top speed of the vehicle is limited by a fixed value?
For each gear separately, of course: I think that is what you want to calculate?

For each gear separately, of course: I think that is what you want to calculate?
Yes I want to calculate the maximum top speed for each gear but how can I limit it if I don't know what the top speed limit for each gear is?

mfb
Mentor
Calculate which speed the 9000 rpm would allow.
Calculate which speed the maximal power would allow.
The smaller value of those two is an upper limit on the achievable speed.
Better: for every rpm value, calculate the corresponding speed and see if your power (as function of rpm) is sufficient to keep that speed. Find the maximal rpm where this works out.

You can do that for each gear separately.

jack action
Gold Member
The top speed in each gear is given by the maximum engine rpm, gear ratio and tire diameter. If there is not not enough power at that engine rpm to support that speed, you have to try a lower rpm, re-calculate the new speed and re-check if there is enough power at that new rpm for that speed, and so on.

The maximum possible speed with a given power is defined here (this speed has to be equal or higher than the calculated speed based on gear ratio and engine rpm).

Calculate which speed the 9000 rpm would allow.
Calculate which speed the maximal power would allow.
The smaller value of those two is an upper limit on the achievable speed.
Better: for every rpm value, calculate the corresponding speed and see if your power (as function of rpm) is sufficient to keep that speed. Find the maximal rpm where this works out.

You can do that for each gear separately.
I understand what you mean now but how do I calculate what top speed the power will allow
The top speed in each gear is given by the maximum engine rpm, gear ratio and tire diameter. If there is not not enough power at that engine rpm to support that speed, you have to try a lower rpm, re-calculate the new speed and re-check if there is enough power at that new rpm for that speed, and so on.

The maximum possible speed with a given power is defined here (this speed has to be equal or higher than the calculated speed based on gear ratio and engine rpm).
Ok that would work for the first three gears and the fifth gear but the fourth and fifth are gears with ratios less than 1. This means I can find limits for the first three gears through engine RPM and for the fifth gear through power but how do I find the limits for fourth gear as the calculations would show it going faster than the horsepower allows at maximum RPM

jack action
Gold Member
Ok that would work for the first three gears and the fifth gear but the fourth and fifth are gears with ratios less than 1. This means I can find limits for the first three gears through engine RPM and for the fifth gear through power but how do I find the limits for fourth gear as the calculations would show it going faster than the horsepower allows at maximum RPM
Assuming there is not enough power with the fourth gear, the fourth maximum rpm is calculated the same way as for the fifth. The maximum speed in those gears might be less than in third gear, as the power available will be less as the rpm drops.

The fact that the gear ratio is less than 1 doesn't make a difference. Anyway, it is the overall gear ratio that counts (selected gear X final drive) and I doubt it would be less than 1.

OmCheeto
Gold Member
What value are you using for drag force?

Lets say through horsepower
Assuming there is not enough power with the fourth gear, the fourth maximum rpm is calculated the same way as for the fifth. The maximum speed in those gears might be less than in third gear, as the power available will be less as the rpm drops.

The fact that the gear ratio is less than 1 doesn't make a difference. Anyway, it is the overall gear ratio that counts (selected gear X final drive) and I doubt it would be less than 1.
Okay the car that can do 9000 RPM is theoretical meaning I don't have real life data for it but I will give you an example of a car for which I know the top speeds in each gear and will show you what I mean because I don't think it will work for the 9000 RPM car.

lets say a car has 75 HP(56kW) of power and revs to a max of 6500 RPM with wheel radius of 0.4572 m. in this case

Car A can do 6500 RPM
Car B can do 9000 RPM (Completely different car, different weight, different engine power etc)

Gear ratios for Car A are:

1st = 3.55
2nd = 1.96
3rd = 1.3
4th = 0.89
5th = 0.71
Final Drive = 4.18

Calculation example for 4th gear at 6500 RPM:
Prop Shaft speed = 6500/0.89 = 7303.4
Wheel speed = 7303.4 / 4.18 = 1747.2
Vehicle Speed = 1747.2 * PI * 0.4572 = 3172.12 m/min
Vehicle speed (MPH) = 118.27 MPH

Calculating maximum vehicle speed from power:
Power = Force*Max Velocity
Frontal area (A) = 2.06 m^2
Drag Coefficient (Cd) = 0.32
Air density (p) = 1.25

Max Velocity = Power/0.5 * A * p * Cd * max velocity^2
Max velocity ^3 = Power / 0.412
Max velocity = (56000 / 0.412)^1/3
Max velocity = 51.4 m/s
Max velocity allowed (MPH) = 115 mph

From real life I know the max velocity calculated for Car A is very accurate because in real life this car would do 113 mph.

Reversing the equations I get the maximum RPM in fifth gear to be 5039 RPM at 115 mph.

So you see the fourth gear calculation tells me the car would do 118 mph which isn't correct as it is past the maximum allowable speed even before shifting to fifth.

Now how do I find out the correct speed in fourth at 6500 RPM as I know the car will definitely hit the rev limiter (6500 RPM) in fourth gear?

I can do the same calculations for the Car B but have no real life data to confirm it hence why I want to get my theory right for the Car A to apply to Car B.

What value are you using for drag force?
Please see my earlier post. The drag force = 0.412*Velocity^2

jack action
Gold Member
Let's go with an example. I'll based it on yours, with a twist to make it more interesting.

Imagine you have an engine with the following power curve:

9kW@2500rpm
12.6kW@3500rpm
16.2kW@4500rpm
19.8kW@5500rpm
23.4kW@6500rpm

The equation for this curve is:

Power (W) = 3.6 * rpm

The limit is 6500 rpm.

The velocity (m/s) that can be reached according to power is:

vP = (3.6 * rpm/0.412)^0.333

The velocity (m/s) according to gear ratio is:

vG = rpm * pi * 0.4672 / 4.18 / 60 / GR
vG = rpm / GR / 174.611

Let's check both velocities at 6500 rpm in every gear:

vP = 38.44 m/s for all gears

vG@GR:

10.49@3.55
18.99@1.96
28.64@1.3
41.83@0.89
52.43@0.71

The first 3 gears are OK, as vG < vP. But we have to reduce the rpm for the 4th and 5th gear and find the new power and the new velocities such that vG = vP. You will find the following:

At 5727 rpm, in 4th gear, vG = vP = 36.85 m/s;
At 4080 rpm, in 5th gear, vG = vP = 32.91 m/s.

So the top speeds in each gear are:

10.49@3.55 (@6500 rpm)
18.99@1.96 (@6500 rpm)
28.64@1.3 (@6500 rpm)
36.85@0.89 (@5727 rpm)
32.91@0.71 (@4080 rpm)

Of course, in reality the power curve might not be modeled easily mathematically and you will have to go by trial and error graphically, but the principle is the same.

Lets say through horsepower

Okay the car that can do 9000 RPM is theoretical meaning I don't have real life data for it but I will give you an example of a car for which I know the top speeds in each gear and will show you what I mean because I don't think it will work for the 9000 RPM car.

lets say a car has 75 HP(56kW) of power and revs to a max of 6500 RPM with wheel radius of 0.4572 m. in this case

Car A can do 6500 RPM
Car B can do 9000 RPM (Completely different car, different weight, different engine power etc)

Gear ratios for Car A are:

1st = 3.55
2nd = 1.96
3rd = 1.3
4th = 0.89
5th = 0.71
Final Drive = 4.18

Calculation example for 4th gear at 6500 RPM:
Prop Shaft speed = 6500/0.89 = 7303.4
Wheel speed = 7303.4 / 4.18 = 1747.2
Vehicle Speed = 1747.2 * PI * 0.4572 = 3172.12 m/min
Vehicle speed (MPH) = 118.27 MPH

Calculating maximum vehicle speed from power:
Power = Force*Max Velocity
Frontal area (A) = 2.06 m^2
Drag Coefficient (Cd) = 0.32
Air density (p) = 1.25

Max Velocity = Power/0.5 * A * p * Cd * max velocity^2
Max velocity ^3 = Power / 0.412
Max velocity = (56000 / 0.412)^1/3
Max velocity = 51.4 m/s
Max velocity allowed (MPH) = 115 mph

From real life I know the max velocity calculated for Car A is very accurate because in real life this car would do 113 mph.

Reversing the equations I get the maximum RPM in fifth gear to be 5039 RPM at 115 mph.

So you see the fourth gear calculation tells me the car would do 118 mph which isn't correct as it is past the maximum allowable speed even before shifting to fifth.

Now how do I find out the correct speed in fourth at 6500 RPM as I know the car will definitely hit the rev limiter (6500 RPM) in fourth gear?

I can do the same calculations for the Car B but have no real life data to confirm it hence why I want to get my theory right for the Car A to apply to Car B.
Well sir, u forgot to consider rolling resistance.