XRAY - Model racing cars

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 Post subject: Gearing by the numbers...Explained
PostPosted: Sun Jul 17, 2005 20:15:27 

Joined: Wed Apr 20, 2005 05:55:51
Posts: 3
Every single car whether it be nitro or electric is going to have a different drive train ratio. Drive train Ratio (DTR) is a value concerning the model's transmission. Your owner’s manual should have this information. The DTR in most cases can't be changed. The ratio between the pinion and spur gear is the Primary Drive Ratio (PDR). Spur/pinion=PDR.

The next step in this process is to determine the Final Drive Ratio (FDR).
PDR*DTR=FDR. Why is this number important? The FDR is used to figure rollout. Rollout is the magic number. When you go to the local track, ask around about each driver's rollout. If they don't know what it is, move on quickly. Once you find a driver in the class you want to race in that tells you his rollout, you will then be able to match your rollout to his as closely as possible. Then the only factors that will affect your lap times are driver skill and power output of the motor. What is rollout? Rollout is the distance the car will travel in one revolution of the motor shaft. Take a shaft car and a belt car with the same exact motor and same exact rollout, and they will have the same exact theoretical speed. The higher the rollout number is, the slower you will be off the line (less acceleration) and the faster the top speed will be.

Tire Diameter*3.14=tire circumference.
Tire circumference/FDR=Rollout

These equations can be used in an Excel spreadsheet. I set up mine so all I enter is the pinion and spur gear value and excel does the rest. If you race at a track that can give you lap times, you can also figure out your speed in MPH (if you know the running track length).

Here are my equations for Excel. Assuming you use row 1 for column headers, These are my headers in row 1.

Spur |Pinion |Tire Diameter |Final Drive Ratio |Rollout |ETS

Spur and pinion columns are whatever combinations you have. I have 4 different spurs and pinions from 18-35.
Tire diameter is a simple number as well. Every pitbox should have a set of calipers. They make measuring tire diameter very easy.
Final drive ratio is this:
=A2/B2*1.77 <------copy and paste to excel in cell D2
Since row 1 is used for column headers, row 2 becomes the first row of values.
A2=Spur, B2=Pinion, 1.77 is the internal reduction of my transmission. Your model may vary.
Rollout is this:
=(C2*3.14)/D2 <------copy and paste to excel in cell E2
C2=Tire Diameter, 3.14 is Pi. The first part of the equation determines tire circumference. D2=Final Drive Ratio
Estimated Top Speed is this:
=((29258/D2)*C2)/336.135 <------copy and paste to excel in cell F2
Keep in mind that this is only an estimate. There are a number of factors that will affect your top speed. 29258 is the rpm listed on my motor label. Check your can or have your motor dyno'd to get this number. 336.135 converts the results to MPH.

The math involved gives distance traveled in inches per one motor revolution(rollout). We want to know actual, not scale, MPH.

5280 Feet per mile
63360 Inches per mile
60 Minutes per hour
Pi(3.14) x Tire diameter = tire circumference
We know that by measuring out lap times how many revolutions the tire makes. And we are measuring in fractions of inches and minutes. Therefore,

63360 / 60 = 1056 (because these numbers will never change)
1056/Pi(3.14) = 336.135 (this number is rounded because pi goes on forever)
This is used only to figure out the theoretical top speed based on your motor rpm under a load. You can also figure out your motor's rpm under load without using a dyno....
For example, the track I race on is 1060 running feet. I turn an average lap time of 42.9 seconds. That's 24.7 feet per second. Or, 16.8 MPH. Now I take this number and reverse this equation

=((29258/Final Drive Ratio)*Tire Diameter)/336.135

and take out the 29258, which is the rpm listed on the can label. And it looks like this:

Known speed in MPH x Final Drive Ratio x 336.135 / Tire circumference = Motor Rpm

16.8 MPH x 6.584 x 336.135 / 7.66= 4854

Now you see that my motor from the factory had a listed 29258 RPM under load, and my track values show that my motor is turning 4854 RPM under load. And yes this motor was cooked

It seems like a lot of confusing numbers and equations, but when you can assign a number to how your car acts on the track, all you have to do is a little simple math to figure out what pinion and spur combination will give you the best lap times.

Changing both the pinion and spur to maintain a consistent ratio will not affect your overall speed or runtime. Using a test setup with one test battery pack, I ran my car with 3 different gear combos, maintaining as close a ratio as possible. For each setup, I ran the battery until it died 3 times then came up with an average runtime and top speed. Guess what, the difference was less than a thousandth of a second. I do have some other thoughts though.
1. For my car (x-ray T1) a taller spur gets my motor lower in the chassis. Gives me better cornering and thus, quicker laps
2. This is a bit of a stretch and might be kind of hard to follow. 93/18 has larger gears and therefore more surface contact between the gears(in the mesh). Now your power plant will put out (x) amount torque at a (x) RPM. That being a constant, having more surface contact between the gears will spread out your motor's applied torque across more of the teeth surface. Granted this is a very small difference, comparable to the rotational mass argument. I'm not sure if this is an accurate statement, but I think that applying the same amount of torque over a larger area would make for a more efficient use of torque.

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