A few handy simple formulas.

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Unforgiven
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A few handy simple formulas.

Post by Unforgiven » Fri Mar 25, 2005 6:03 pm

Hey all, just thought I would share a few simple formulas with everyone that should make it a little easier to figure out gear ratios and get a rough estimate of how fast an engine will go given the RPM, gearing and tire size.


Gear ratios

Ok, the first formula will calculate the drive ratio between two gears(example Clutch bell and Spur gear)
The formula is as follows
driven(# teeth) divided by drive(# teeth) = drive ratio

So for example we know the stock Savage gearing is 15T clutchbell(this is the drive gear) and 49T spur gear(this is the driven gear).... so we would simply divide 49 by 15 to arrive at the drive ratio.

49 / 15 = 3.26666666
we'll just round it up to 3.267
then we simply append a ":1" to the end to make it 3.267:1
We'll call this our "engine ratio"
what this means is that the driven gear is making 1 complete revoloution for every 3.267 revoloutions of the drive gear

Ok, next let's do the axles, we know that the axles are driven by a 13T pinion that is driving a 43T ring gear.

43 / 13 = 3.30769
we'll just round it up to 3.308 to get a drive ratio of 3.308:1
Now we have the drive ratio of our axles.


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Next up I'm going to show you how to calculate the Final drive ratio

to do this the formula is as follows
engine ratio * tranny ratio * axle ratio = final drive ratio

You simply take the engine ratio that we just calculated above with the CB and spur and multiply it by the internal tranny ratio and then multiply that by the axle ratio that we also just calculated above and this will be your "final drive ratio"

Now I know what you're thinking, "i'm not takin my tranny apart just to count the teeth on all the gears only to confuse the hel* out of myself!!!"..... well never fear, I thought the same thing, but there are a few places that have the internal tranny ratio for the Savage already figured out for you........ I pulled them out of an old issue of RCCA when they did a "drive test" of the Savage 25

according to RCCA, the tranny internal drive ratios for the savage 25 are as follows
1st gear - 2.215:1
2nd gear - 1.537:1

I'll just take their word for it for now! :wink:

Ok, so here is the information we have so far

engine ratio - 3.267:1
tranny 1st gear ratio - 2.215:1
tranny 2nd gear ratio - 1.537:1
axle ratio - 3.308:1

and remember what I said the formula was?
engine ratio * tranny ratio * axle ratio = final drive ratio

So first we'll see what our final drive ratio is for 1st gear
3.267 * 2.215 * 3.308 = 23.93802

we'll just round that down to 23.938 to get a "final drive ratio" of 23.938:1 in 1st gear.
What this means is that while in 1st gear your wheels are making 1 complete revoloution for every 23.938 revoloutions of the engine shaft


Ok, now let's see what we get for 2nd gear
3.267 * 1.537 * 3.308 = 16.61072

ok, we'll just round it up(if you were paying attention you'd know i was gonna say that!)to 16.611 for a "final drive ratio" of 16.611:1 in 2nd gear.


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Ok, now for the fun part........finding out how FAST it will go!!!!
To do this, we use the following formula. :twisted:

engine rpm divided by final drive ratio * tire circumference(dia in inches * 3.141) divided by 12(inches in a foot) * 60(minutes in an hour) divided by 5280(feet in a mile) = estimated speed in MPH

In order to lessen confusion I'll disect this formula and explain step by step what's going on.

engine RPM - This formula will be most accurate if you know the actual Max RPM under load...... not necessarily the manufacturers *claimed* max RPM, ok, the stock .25 engine is claimed to have a max RPM of 38000, but when you apply this number to the formula it just don't jive with how fast we know a Savage is...... 30000 seems to plug in much better.... so we'll just assume 30000RPM here as our max RPM under load.

final drive ratio - By figuring in the final drive ratio that we just calculated above, we know how fast the wheels are turning in relation to the engine..... dividing the engine RPM by this number will give us the actual RPM that the wheels are spinning at.

tire circumference - To get this figure you would simply multiply the tire diameter(in inches) by the fixed variable 3.141........ the value you arrive at is actually how far the truck will travel(in inches) for every complete revoloution of the wheels, if we multiply engine RPM by final drive ratio and then multiply that figure by tire circumference we arrive at a figure that tells us how far the truck has travled(in inches) in one minutes time!

fixed variable 12 - We know that there are 12 inches in a foot, so if we take the figure we arrived at from our last step and divide it by 12 we can tell how many feet the truck travled in one minute.

fixed variable 60 - We know there are 60 minutes in an hour, so by multiplying the figure we arrived at from our last step by 60 we know how many feet the truck travled in one hour.

fixed variable 5280 - We're almost home! We know that there are 5280 feet in one mile, so by dividing the figure we arrived at in our last step by 5280, we now know how many miles the truck travled in one hour..... and this of course is your estimated speed in MPH.

Ok, so let's regroup and gather the information we have so far.

engine RPM - 30000
final drive ratio 1st gear - 23.938
final drive ratio 2nd gear - 16.611
tire diameter - 6 inches

The first thing we need to do is calculate our tire circumference
6 * 3.141 = 18.846


ok now we divide our engine RPM by our final drive ratio to get our "wheel RPM".
30000 / 23.938 = 1253.237


now we need to multiply our wheel RPM by our tire circumference to arrive at how many inches we've travled in one minute.
1253.237 * 18.846 = 23618.504


now divide the distance travled in inches by 12 to get the distance travled in feet.
23618.504 / 12 = 1968.209


now we multiply our distance travled in feet by 60 to get our distance travled in feet in one hour.
1968.209 * 60 = 118092.54


and lastly we divide our distance travled in feet in one hour by 5280 to arrive at our distance travled in miles in one hour which tells us our speed in MPH.
118092.54 / 5280 = 22.37
and we get 22.37MPH

and now you know how fast the truck can go if it stayed in first gear and never shifted into second.


Ok, now let's find out what it can do in 2nd gear
30000 / 16.611 * 18.846 / 12 * 60 / 5280 = 32.23

so the truck tops out at 32.23MPH in second gear with stock engine, gearing, and tires.......... and there ya go!


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Ok, now I can't make any claims on the accuracy of any of this data or even the formulas, I'm not an engineer or a mathamatician and it's VERY possible that there's something I'm missing or something I'm just plain wrong about, I didn't cut and paste these formulas from a website or out of a magazine, these are my own figurings and as ANYONE can tell ya....... I'm NO GENIUS! :twisted:

On the speed formula, if you use the engine manufacturers claimed max RPMs you will usually end up with a highly exagerated figure because that figure usually assumes there is no load on the engine, so use your own best judgement..... there's still no replacement for a radar gun when trying to determine top speed, but I think these formulas should be very helpfull when trying to determine how large an effect a gearing change or change in tire diameter or going to a different engine will have on your truck...... and anyway it's just FUN trying to figure out what these changes will do!

Have fun! :D

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