Formula for calculating car speed in km/h ?

[Dan1891]

I was thinking it would be fun to have a formula to calculate car speed in km/h.

Given motor rpm, pinion teeth, spur teeth and tire diameter in mm.

I'm not good enough on the math  But someone else maybe? Or know such a formula already?

[El Gecko]

Sure, the math is there if you want to take the time to discover it, but it's probably easier to just measure (with a GPS bicycle computer)

[Pylon80]

As an aerospace engineer I deal with the question of "how fast will this go?" all the time. The physics are straightforward enough but the actual data can only be measured and approximated (which we then call a model). The only formula one could come up with would be a "rule of thumb" based on empirical data  You would need a lot of cars and run a lot of test and search for trends and identify the parameters that make the biggest difference in the results. The motor's effective KV, battery voltage and actual rollout would certainly be good parameters. Type and size of tires would be another one. Then you might come up with a formula that will provide an approximative answer for various body shells. Maybe someone did that already? That would be fun indeed.

As @El Gecko said it would be much easier and faster to just try it and measure  All the speed run guys are using the little SkyRC GPS.

In terms of physics: any vehicle's top speed will be that at which the propulsive force is exactly equal to the sum of all the forces trying to slow it down. The interesting point is that 1) the propulsive force available varies with speed  - there is a point where the motor/battery/ESC will be making the most power; for instance at very low speed a motor will be getting very hot and not making much power. 2) At the same time the forces trying to slow the car down all increase with speed (bearing drag, tire drag and aerodynamic drag). Somewhere in the middle is your answer.

[Dan1891]

Well, i was more thinking of a formula of the theoretical speed

I understand in real world this isnt gonna be correct, but at least in the ballpark or so! 

[Honza]

first you need to get FDR - spur teeth count/pinion teeth count * internal ratio.

Wheel RPM is calculated by dividing the motor RPM with FDR - divide that with 60 to get rotation per seconds. That is multiplied by wheel circumference in meters to get speed in meters per seconds.

That only gives you theoretical speed with no load. Real speed will be much lower due to drag - which we don't know. We don't even know motor parameters - some older Tamiya motors had nice graph on the box with torque, power and efficiency, which would help.

[Dan1891]

2 minutes ago, Honza said:

first you need to get FDR - spur teeth count/pinion teeth count * internal ratio.

Wheel RPM is calculated by dividing the motor RPM with FDR - divide that with 60 to get rotation per seconds. That is multiplied by wheel circumference in meters to get speed in meters per seconds.

That only gives you theoretical speed with no load. Real speed will be much lower due to drag - which we don't know. We don't even know motor parameters - some older Tamiya motors had nice graph on the box with torque, power and efficiency, which would help.

Thnks! Now i THINK i can get some formula up.

Hmm, internal ratio, is that some added gearbox you mean?

 

[alvinlwh]

I use this app, it is pretty spot on.

https://play.google.com/store/apps/details?id=redscrew.gearcalc

 

[Dan1891]

26 minutes ago, alvinlwh said:

I use this app, it is pretty spot on.

https://play.google.com/store/apps/details?id=redscrew.gearcalc

 

Wow! Now we talking!  I wish it was in km/h though, but "you cant always get what you want"! (as Stones sung so well)

[alvinlwh]

9 minutes ago, Dan1891 said:

Wow! Now we talking!  I wish it was in km/h though, but "you cant always get what you want"! (as Stones sung so well)

Here is how accurate it is.

 

 

[Dan1891]

2 hours ago, Honza said:

first you need to get FDR - spur teeth count/pinion teeth count * internal ratio.

Wheel RPM is calculated by dividing the motor RPM with FDR - divide that with 60 to get rotation per seconds. That is multiplied by wheel circumference in meters to get speed in meters per seconds.

That only gives you theoretical speed with no load. Real speed will be much lower due to drag - which we don't know. We don't even know motor parameters - some older Tamiya motors had nice graph on the box with torque, power and efficiency, which would help.

I had to try this on my old Datsun 280ZX:

Pinion=15

Spur=40

Internal ratio=1 ( i think the Datsun has no)

FDR=40/15=2.666

Motor RPM=16300

Wheel RPM=16300/2.666=6114

RPS=Wheel RPM/60=6114/60=101.9

Tire diameter= 53mm

Tire circumference = pi*diameter = 166.5mm = 0.1665m

meters per second=RPS*Tire circumference in meters=101.9*0.1665=16.96

km/h = meters per second * 3.6 = 16.96*3.6 = 61.1 km/h

WOW, my old Datsun runs in 61.1 km/h then!! ( if i have done the calculation right) 

Theoretical then of course.

 

 

[Fabia130vRS]

https://www.radiocontrolinfo.com/information/rc-calculators/rc-car-calculator/   (brushless)

 

Using this one a lot of times. works good

[OoALEJOoO]

@Dan1891 Your calculation above for theoretical top-speed looks correct. The trick in calculating the real top-speed is estimating losses (friction, wind, rolling, etc). Not sure if any of the above cited calculators do so, but if they are accurate with real-world measurements, then I guess they do account for them.

I had my swing at the whole calculation some time ago and went beyond just calculating top-speed. To me the interesting bit was to calculate acceleration and FDR cross-over points. From this you can derive distance vs. speed curves, which is probably the best tool to understand what FDR to use in a particular track (since you know the distance of each straight). More info on my progress so far on this thread:

Theoretical Speed & Distance Curves - General discussions - Tamiyaclub.com

Haven't made any progress in over a year though

[alvinlwh]

13 hours ago, Dan1891 said:

 I wish it was in km/h though, but "you cant always get what you want"! (as Stones sung so well)

You can get what you want.

 

[alvinlwh]

14 hours ago, Dan1891 said:

Pinion=15

Spur=40

Internal ratio=1 ( i think the Datsun has no)

FDR=40/15=2.666

2.6 is quite extreme and will probably burn out most motor. I did 2.4 on my 3R M4 (similar M sized wheels as yours), got nowhere near the 50+mph and melted the silver can in just one battery pack.

In fact, it did worse top speed with this insane ratio than a more sensible ratio (that still melted the motor).

 

[Honza]

15 hours ago, Dan1891 said:

WOW, my old Datsun runs in 61.1 km/h then!! ( if i have done the calculation right) 

Theoretical then of course.

More precisely, it can spin the wheels at that speed, if you manage to reduce internal friction to zero. That's due to parameters of electric motors - at maximum RPM, its torque is zero. At zero RPM, torque is at its maximum. In the middle, there's maximum mechanical power input, which is where you want to aim, if you want to reach full potential.

[Dan1891]

5 hours ago, alvinlwh said:

2.6 is quite extreme and will probably burn out most motor. I did 2.4 on my 3R M4 (similar M sized wheels as yours), got nowhere near the 50+mph and melted the silver can in just one battery pack.

 

I dont think thats a problem with my motor, because i ran it plenty at 2.666 back then (its an old car) without burning it.

2.666 was one of 4 ratios you could choose on it.

Looking in the manual(found a pdf of it!): the 4 ratios where: 3.23, 2.928, 2.666, 2.437

But i only have the 2.666 combo left

[joeling]

1) To get circumference of tire = pi (3.142) X Diamter of tire

2) to get rpm of motor = KV rating of motor X battery voltage of battery pack

3) gear ratio = final drive ratio (some buggies provide this number) X spur teeth number divided by pinion teeth number

4) distance travelled in 1 hour (km/h) = rpm divided by gear ratio X circumference of tire X 1000000 (to convert mm to km) X 60 (minutes)

 

Expansion on final drive ratio for 3 diff vehicle = teeth of diff ring gear divided by teeth of diff pinion

[alvinlwh]

2 hours ago, Dan1891 said:

 

I dont think thats a problem with my motor, because i ran it plenty at 2.666 back then (its an old car) without burning it.

2.666 was one of 4 ratios you could choose on it.

Looking in the manual(found a pdf of it!): the 4 ratios where: 3.23, 2.928, 2.666, 2.437

But i only have the 2.666 combo left

Is it a direct drive as in pinion to spur to wheels with no more gears in between?

Like these?

What is the motor? I will love to get one of them.

[Dan1891]

15 minutes ago, alvinlwh said:

Is it a direct drive as in pinion to spur to wheels with no more gears in between?

Like these?

What is the motor? I will love to get one of them.

Yes, like in your last picture. Just a pinion and a spur.

Its an RS-540SD black motor.

[alvinlwh]

15 minutes ago, Dan1891 said:

RS-540SD black motor

Hmm, interesting, about the same RPM as a LT but next to no torque at all. Maybe I will stick my LT in with that 2.4 ratio and see what happens.

[Tamiyastef]

Nice. Another app added to my phone