TOPIC:

'Cause i was collecting needed formulas to calculate what i need for the car, i thought it would be a good idea to create a sticky here to collect all needed formulas in R/C.
Maybe someone knows more and can add them.

RPM/kV/V:

• RPM = kV * V (Example: 23.000 RPM = 3194 kV * 7,2 V)
• kV = RPM / V
• V = RPM / kV

Watt/Volt/Ampere:

• A = W / V (Example: A motor with 184w running with 7,2V needs about 26 A from the battery, over the cable, over the connectors, over the ESC)
• W = V * A
• V = W / A

The Gearbox:

• Inner motor ratio = Diff-Gear / Counter-Gear(Idler or Pulley) (This can be more complexe at belt-driven cars with more than 2 belts)
• Gear-Ratio to the motor = (Maingear / Piniongear) * (Inner motor ratio)
• RPM on Axle = (kV * V) / Gear-Ratio
• Meter per wheelturn = (Wheel diameter in mm * 3,14159 (PI)) / 1000
• Meter per second = (RPM on Axle * Meter per wheelturn) / 60
• theoretical max km/h = Meter per second * 3,7
• Shorter form for max km/h = ((kV * V) / ((Maingear / Piniongear) * (Inner motor ratio)) * ((Wheel diameter in mm * 3,14159 (PI)) / 1000)) / 60
  
• theoretical max mp/h = max km/h * 0,621
• newtonMeter on axle = W / (kV/60 * 6,28)

Please don't hasitate to correct mistakes! Also add formulas for miles please. Maybe someone knows how you can calculate nM on wheels and also relation between wheel diameter and gearratio. For eg bigger wheels need 1-2 pins less on pinion gear than smaller wheels.

I think it's a great initiative.
We'd need some more explanation and possibly a legend for newbies to understand as well...
I had a few attempt at similar posts. Can get complicated quickly.

www.tamiyabase....Itemid=476

I wrote:

I've been doing some theoretical calculations to see if the set up for the Manta Ray will be suitable.
First thing is to determine the internal gear ratio. Of course this is not a set value since the pinion and spur gear can be varied.

It follows this calculation :

Z₁ = # teeth pinion
Z₂ = # teeth spur gear
Z₃ = # teeth idler gear (= 16)
Z₄ = # teeth differential (= 39)

Gear ratio = (Z₂/Z₁) * (Z₄/Z₃) = (Z₂/Z₁) * (39/16) = (Z₂/Z₁) * 2.4375

This translates into the following overview :

I think I will be using a 21T pinion and a 69T spur.
This will make the gear ratio (69/21) * 2.4375 = 8.0

Using an Lrp motor that can do 31000 rpm this gear ratio will give (31000/8) = 3875 rpm on the wheel axle.
This is of course the same rotation speed a the wheel will make.

I am using 30 series Pro-Line tyres which have a diameter of 100mm = 0.1m.
The circumference of this wheel is (pi * diameter) = (3,14 * 0.1) = 0.314m.

Making 3875 rotations a minute, the distance travelled (of the outer edge of the wheel) will be 3875 * 0.314 = 1218m.
Which translates to (1218m/60sec) = 20.3 m/s = 73 km/h.

So this is the theoretical top speed the Manta Ray will have with this set up.

When using a Orion motor (thank you Lars) with 40000 rpm, a 25T pinion and the 66T spur, the car would do 115 km/h.

Tbh, I never really got how wheel size plays in exactly... until last night.
Thing is, when a fabricator says recommended gear ratio is such and such, this is directly related to the wheel size of the car the motor is generally meant for. But there is almost never an exact mention of what this would be.
I always thought you had to gear the car higher because of off road circumstances but is it mostly because of wheel size.

I'll take 62mm for 1/10 on road and 87mm for off road. The factor is 87/62 = 1.4.
So if a motor is run on road at 1:6 gearing (and this is the only known spec), you can run it off road if you gear it 1:(6x1.4) = 1:8.4.
Really, fabricators should give general info. Something like "this and that ratio at 100mm wheel size".

This means there is a linear relationship between wheel size and pinion size.
If for example you want to increase the diameter of the tyre by 20%, you'd have to go down 20% in pinion size as well.
In the simplest setup, because there may be other gears one can vary to influence the final ratio...

I'll see if I can calculate expected Nm of the motor towards wheel size.
Interesting subject. The kind that can temporarily blow your mind though.

Yeah, size of wheels is heavy important at real size cars! You can't just change them, you have to get the gear for it to use it (also you have to setup the speedometer). I always try to transfer my knowledge of motorsport to the r/c's

Edou, about your factor of 1.4. At my LRP there are infos about on/offroad setup. 17T: 6,6/8 = 1,21~ & 12T: 8/10,4 = 1,3. It's near 1.4 but not 1.4.
Also what is "onroad" and what is "offroad"?
Offroad: Buggys has ~87mm. Monsters have >115mm and ShortCourse has anything between. Also you can drive just dirt, grasland or heavy terrain. You can have a track with many jumps and corners or just an oval track with high speed.
Onroad: You can ride a rough plain street, a flat parkslot or a very flat indoor track with multiple curves. Wheels imho always 62mm onroad but made of different rubber.

I think a factor of 1.2-1.4 is a safe thing to have a harmless setup. The rest is testing, testing, testing.

Inner resistance of the car is also a factor. More gears will means you need a higher ratio.
With direct drive formula cars, the wheel size is the same as on road but you can use a much lower gearing on these cars.

I wrote:

I'll see if I can calculate expected Nm of the motor towards wheel size.

I've looked into this but the given torque numbers are in no case reliable.
Probably we need "stall" data for all motors and not this elusive "torque at maximum efficiency".
That seems to be in the same range for just about every motor...
I do believe you have to gear up when going down in motor turns because loss of efficiency seems to be unavoidable.
Even if this "dynamic" torque seems to be the same, lower turns motors have more trouble with fluctuating torque demand.
Thus needing a transmission that's easier on them...

No reason to leave out the basics of torque though...

What is torque?
It's basically leverage - a force applied over a certain length.
Force is usually measured in Newton (N).
10 Newton can be compared to the force with which the earth is pulling on 1 kilogram.

Now let's say that length (the lever arm) is 100mm and the force applied is 1N :



The torque that results from this is (lever arm x force) = (100mm x 1N) = 100mmN = 100Nmm.

Now how does this translate to RC motors?
The torque they can produce is a given (although not often known exactly in practice).
But take for example a silvercan that can produce 200 Nmm at some point...
That means the length of the blue line times the force represented by the black arrow should be 200 Nmm :



Meaning if the blue line were were a 25mm long rod, the motor could produce 8 Newton of force at the end of it.
Now imagine that blue line is actually the radius of the wheel on your car, directly attached to the motor...
It would be the same as hanging 800 grams (8N) on it :



Of course normally there is a transmission in between. A silvercan would soon die when used 1:1.
Let's take a transmission that has a 10:1 gear ratio (on the safe side)...
Now the lever arm will effectively only be 2.5mm for the motor - and there's 80N force it can produce over that length.
This is because total torque (arm times force) stays the same.
The wheel will also turn ten times slower as a result.

Needless so say there's much more to this subject - angular velocity, inertia, angular momentum...

en.wikipedia.org/wiki/Torque

If anyone can put together a formula for gear ratio (that I can understand) I might be able to make an online calculator for this.

-Lars

larbut wrote:

If anyone can put together a formula for gear ratio (that I can understand) I might be able to make an online calculator for this.

-Lars

I have the formulas in excel and it won't be any problem for me to put this into some php classes. Is there any interface description of this board, to put API/Plugins/whatever into it?

funkindemup wrote:

larbut wrote:

If anyone can put together a formula for gear ratio (that I can understand) I might be able to make an online calculator for this.

-Lars

I have the formulas in excel and it won't be any problem for me to put this into some php classes. Is there any interface description of this board, to put API/Plugins/whatever into it?

There is already a Joomla module available that makes any (?) formula calculate on Joomla sites. I have not tried it yet, but if you send me the Excel sheet, I can give it a try.

-Lars

My wife is blocking my pc... I'll send you the Excel asap