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

[mvrick208]

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.

[Black Lotus]

Mechanical speeds in gears that are NOT drag limited with no tire slippage.

RPM /(divided by) 168 (the constant) / Rear Gear ratio / Internal Transmission ratio X Tire Radius.

So, my old Corvair went like this for 1st gear--
6000 / 168/ 3.55 / 3.11 X 11".
=35.58 MPH

Also, aero drag increases by the cube.
And good luck finding the coefficient of drag (Cd) for your car. And the frontal area is not a piece of cake to get either.
Probably work up some data by doing a coastdown test for your particular car.

Or you could just take your car out to a back alley and floor it...

[mvrick208]

Originally Posted by Black Lotus

Mechanical speeds in gears that are NOT drag limited with no tire slippage.

RPM /(divided by) 168 (the constant) / Rear Gear ratio / Internal Transmission ratio X Tire Radius.

So, my old Corvair went like this for 1st gear--
6000 / 168/ 3.55 / 3.11 X 11".
=35.58 MPH

Also, aero drag increases by the cube.
And good luck finding the coefficient of drag (Cd) for your car. And the frontal area is not a piece of cake to get either.
Probably work up some data by doing a coastdown test for your particular car.

Or you could just take your car out to a back alley and floor it...

I already have the frontal area and the coefficient of drag on the car. We are designing Formula student car so these factors are already known therefore I can calculate the drag force.

Can you tell me where you got the constant 168 from and what it represents?

Also if the speed is not drag limited does this mean I can fit a massive flat board on my car to increase drag force and given an infinite and straight road it will reach the same top speed as it would without the massive flat board at the front?

[Black Lotus]

Can you tell me where you got the constant 168 from and what it represents?

Don't know where I got it, probably a car magazine from the 60s. There is a lot of necessary numbers juggling to get from A to Z in that formula--168 rolls it all together. I never bothered to break it down. You can if you want.

Also if the speed is not drag limited does this mean I can fit a massive flat board on my car to increase drag force and given an infinite and straight road it will reach the same top speed as it would without the massive flat board at the front?

By the definition of the term "not drag limited" it will.
However, if it wasn't drag limited before adding the flat board, it may be now.
If a car is not aero drag limited in it's top speed capability, it means that there is a mechanical or other limitation to it. Namely- the car is so unstable that the driver doesn't want to push it any faster, the engine reaches a given speed (redline on the tach) and the drivers lifts off the gas, or the engines rev limiter cuts the power.
Or there is a police blockade in your alley.

[Stealthee]

Originally Posted by mvrick208

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.

Horsepower doesn't affect the top speed in given gears unless a car cannot reach the gear limited speed. For instance in 91-93 3000GT VR4's the gear limited top speed is ~208 mph. The car is horsepower limited and cannot reach that speed, but that doesn't affect the theoretical top speed of the given gear as it is a constant.

The formula I have seen for calculating top speed in a given gear is

(RPM x tire diameter in inches)/(final gear ratio x 336)=speed in gear

You figure final gear ratio by figuring overall reduction ration x gear reduction ratio.

So if your final drive is 3.73 and your gear ratio for 5th gear is .70 you multiply 3.73 x .70 to get 2.611

Then lets assume a 6000 redline with 245/45/17 tires you'd have

(6000 x 25.7)/(2.611 x 336) = 175 mph top speed

Again, just because a gear can do 175 mph, doesn't mean the car has the power to reach those speeds. The main reason is for low RPMs while highway cruising.

[mvrick208]

Originally Posted by Stealthee

Horsepower doesn't affect the top speed in given gears unless a car cannot reach the gear limited speed. For instance in 91-93 3000GT VR4's the gear limited top speed is ~208 mph. The car is horsepower limited and cannot reach that speed, but that doesn't affect the theoretical top speed of the given gear as it is a constant.

The formula I have seen for calculating top speed in a given gear is

(RPM x tire diameter in inches)/(final gear ratio x 336)=speed in gear

You figure final gear ratio by figuring overall reduction ration x gear reduction ratio.

So if your final drive is 3.73 and your gear ratio for 5th gear is .70 you multiply 3.73 x .70 to get 2.611

Then lets assume a 6000 redline with 245/45/17 tires you'd have

(6000 x 25.7)/(2.611 x 336) = 175 mph top speed

Again, just because a gear can do 175 mph, doesn't mean the car has the power to reach those speeds. The main reason is for low RPMs while highway cruising.

Thats what I meant to ask, the calculation gives you 175 mph but the car might have a real top speed of 140 mph. Using power =Fv equation I can come up with a pretty accurate top speed for whatever car I have tried but I just don't know how to calculate the top speed in each gear that the car can do. I will give you an example:

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


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

(In real life the car can do around 95-100 mph at 6500 RPM in fourth gear)

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 know you have said horsepower doesn't affect top speed in given gears but how do I calculate the correct speed the car can do in each gear given its characteristics? For gears upto third gear I get pretty accurate numbers but then the overdrive gears (4th and 5th) give me ridiculously high speeds.

[Stealthee]

You are mistaken. The speed is unchanged by the gear ratio.

In your calculation you do not have tire diamter which does affect the gear ratio.

Let's just say though that in your example car it has the gearing to reach 115mph in 4th gear at 6500 rpm, but not the power to reach that 115mph. The car will NEVER reach 6500 rpm in 4th.

The gear ratio to speed is a fixed number.

In my example about the VR4 it has the gearing to hit 208 mph at 7300 rpm in 5th, but not the power. That means it will not hit 7300 rpm. Most guys have achieved a top speed of ~170 mph. That means they only hit approximately 6000 rpm.

[mvrick208]

Originally Posted by Stealthee

You are mistaken. The speed is unchanged by the gear ratio.

In your calculation you do not have tire diamter which does affect the gear ratio.

Let's just say though that in your example car it has the gearing to reach 115mph in 4th gear at 6500 rpm, but not the power to reach that 115mph. The car will NEVER reach 6500 rpm in 4th.

The gear ratio to speed is a fixed number.

In my example about the VR4 it has the gearing to hit 208 mph at 7300 rpm in 5th, but not the power. That means it will not hit 7300 rpm. Most guys have achieved a top speed of ~170 mph. That means they only hit approximately 6000 rpm.

I did take the tire radius into account though when calculating vehicle speed.

But the car does reach 6500 RPM in fourth gear. It doesn't reach 6500 RPM in fifth gear though which I get is the limit. Like you said it has been geared to reach higher speeds but limited by power. What I want to know is how to calculate the top speed in fourth gear when the car does reach 6500 RPM because it actually does hit 6500 RPM in fourth gear in real life. The calculation shows the car is geared to reach 118 mph and 140 mph in 4th & 5th respectively.

[Stealthee]

Originally Posted by mvrick208

I did take the tire radius into account though when calculating vehicle speed.

But the car does reach 6500 RPM in fourth gear. It doesn't reach 6500 RPM in fifth gear though which I get is the limit. Like you said it has been geared to reach higher speeds but limited by power. What I want to know is how to calculate the top speed in fourth gear when the car does reach 6500 RPM because it actually does hit 6500 RPM in fourth gear in real life.

Use the calculation I posted. It works.

In 4th gear the final drive would be

(.89 x 4.18) = 3.7202

So now the only number missing is tire diameter in inches

(6500 x tire diameter)/(3.7202x 336) =

EDIT: Another thing to consider is your math shows 115 mph,but your own experience showed 113, but have you considered the speedometer being off? Many car speedometers are slightly inaccurate, especially at higher speeds.

[mvrick208]

Originally Posted by Stealthee

Use the calculation I posted. It works.

In 4th gear the final drive would be

(.89 x 4.18) = 3.7202

So now the only number missing is tire diameter in inches

(6500 x tire diameter)/(3.7202x 336) =

EDIT: Another thing to consider is your math shows 115 mph,but your own experience showed 113, but have you considered the speedometer being off? Many car speedometers are slightly inaccurate, especially at higher speeds.

you're right the calculation you gave works better as it gave 117 mph in fifth which isn't far off.

Also I have already taken into consideration the inaccuracy of the speedo. It actually shows 115 mph on the speedo and it is off by 2 mph for every speed so 115 - 2 = 113 mph.

btw I like your GTO

[Stealthee]

Thank you for the compliment. Sadly it is not that pretty at current time, but I have gotten motivated to get started on it again and hopefully it will be even better in the end.

[mvrick208]

Originally Posted by Stealthee

Thank you for the compliment. Sadly it is not that pretty at current time, but I have gotten motivated to get started on it again and hopefully it will be even better in the end.

No problem and thank you for your help. Also good luck with the car mate

[JoeDeJong]

Originally Posted by Black Lotus

. And the frontal area is not a piece of cake to get either.
Probably work up some data by doing a coastdown test for your particular car.

Or you could just take your car out to a back alley and floor it...

The Coastdown test is a good idea. Make note of your curb weight too. When you do your coast down use a stop watch and press the lap button for every 10mph so you can get a good chart of resistance.