# How to calculate a car's velocity from given RPM and Torque?

1. Sep 30, 2009

### dehseth

Hey guys,

I am kinda simulate car dynamics with given parameters. I actually want simple solution. I have been doing research for a couple of days and here's what I got till now:

First of all I want use metric system. (km/h, sn, kg, Nm etc...)

Now I have RPM and Torque values. Here's what I did to calculate linear velocity of car at given RPM and torque:
1. I have converted (lb ft) torque values to (Nm)
2. I have calculated transmission output torque using gear ratio.
3. Assuming car has moment of inertia value 50 (I guess it is ok, isn't it?) I have calculated Angular Acceleration
4. Assuming car has a wheel with radius 0.5m, I have calculated Linear acceleration.
5. Then I have calculated linear velocity, assuming time 1 sec.

So is it correct? anything I miss? did wrong? Any suggestions like to this change this to that??

Any help is appreciated, thank you.

Last edited by a moderator: May 4, 2017
2. Sep 30, 2009

### xxChrisxx

I dont get why you've got an anglular acceleration from MOI?
Then used that to find a linear acceleration.

Also how much detail do you need, can you assume a perforct rolling wheel with no slip?

3. Sep 30, 2009

### Bob S

Hell dehseth-
There are only two things you need both RPM and torque (= power) for:

1) Acceleration, and

2) To replace energy lost (to heat), primarily for air drag (goes as velocity cubed) and tire rolling resistance.

Power (watts) = torque (Nm) times RPM x 2 pi/60

Bob S

4. Sep 30, 2009

### dehseth

Thank you for your replies guys...

What I want is to calculate instant linear accerelation (and linear velocity) of a car using torque and RPM. So I tried to calculate it bu doing those steps.

@xxChrisxx On the internet resources I saw that torque = MOI * angular acc. So I divide it.

@Bob S How can I calculate linear accerelation (and resistances will be perfect if I can calc them also) using power, torque, RPM?

Thank you.

5. Oct 1, 2009

### xxChrisxx

Ok, MOI doesn't apply in this case as you aren't trying to rotate the car.

Its also much much easier to get speed than you are doing.
You can get speed from RPM * gear ratio * wheel circumfrence.

Why do you think this is?

There are a couple of methods as to how to calcualte the acceleration. One involves torque and the other involves Power.

Details can e seen here

6. Oct 1, 2009

### dehseth

I have posted a question to that topic and in case I do not get any answer in there I would like to copy it here also:

1. What's primary and final gear ratio? And how it is related with gear ratio? Is it some kind of a motorcycle special thing?

2. While calculating over all ratio (at cell D15) why ratio is multiplied by 12 (what is the meaning of this constant)

3. While calculating over all ratio (again) why ratio is divided by wheel radius?

4. During calculation of accerelation (at cell H19), the value is divided by 32.2. Why?

I may not get constant values beacuse of metric system. :uhh:

7. Oct 1, 2009

### xxChrisxx

1.

Gear ratios are what you get in a gearbox and the things you change.

Final drive is after the power has gone through the gearbox and speed has been reduced, it is futher reduced by a set amount by the differential. So in effect it is multiplying each gear in the gearbox by this amount.

I'm not sure what a primary gear ratio is because i'm unfamiliar with bikes, I can only assume is a speed step down before it goes into the gearbox.

To get total gear ratio you just multiply all three together. This provides the rpm reduction by that amount and the torque increase by that multiplier.

2.
For some reason I cant acutally see the multiplied by 12 bit.

The wheel itsself is infact a gear. If you put a larger diameter wheel for each revolution the fruther you will go.

3.
I can't see this.

4.
I think I may be looking at a different sspreadsheet to you.

8. Oct 1, 2009

### dehseth

But you need to make a copy of it from file menu to see formulas. And you should make formula bar visible from view menu to see cell formulas.

If I go over questions:

1. I am using gear ratios as: 3.54, 2.13, 1.36, 1.03, 0.72 Should I be multiply these values with some kind of primary ratio? (I do not have much knowledge about car gears)

2. 3. On cell D17 the calculated first gear ratio is multiplied by 12 and divided by wheel's radius. Why is it multiplied by 12? And why did it divided by wheel's radius?

4. At cell H19, during calculation of accerelation; the wheel's output torque is divided by mass of motorcycle and and result is divided by 32.2. Where does 32.2 come from?

Thanks..

9. Oct 1, 2009

### xxChrisxx

Its Primary ratio * Chosen Gear Ratio * Final Drive.

So in the case of the bike with 1st gear selected.
2.09 * 2.46 * 3 = 15.42
15.42 is the total drive ratio in 1st.

For 2nd gear its
2.09 * 1.78 * 3 = 11.42

2. This is explained on row 29. It appears to be a correction factor for torque and wheel radius.

3. 32.2 is the acceleration by gravity in ft/sec^2. It's getting the vehichle mass from its weight in cell c25.

10. Oct 1, 2009

### dehseth

Okey so 32.2 is 9.8m/sec^2 for me. to find mass value.

And I guess 12 is correction of wheel raidus to be clear. I think he just wanted to discard wheel radius bu making result 1 (12/12).

For the first question I get abou multiplying. He just multiplied primary * gear * final values to find real gear ratio. But I wanna make a car simulation and my gear ratios are different and I do not have any primary or final ratio on my hands... Should I find smt like primary ratio multiplier for cars or smt? Do you have anything about that?

Thank you so much for your help.

11. Oct 1, 2009

### dehseth

12. Oct 1, 2009

### Naty1

dehseth posts:
Did you draw any conclusion?

It would seem to me to depend on what you are trying to do and the degree of accuracy you are seeking.

13. Oct 1, 2009