Several people have asked me lately how
to calculate speeds in gears or engine rpm at a given
speed. These calculations aren't complex but they do
involve a few steps. The first step is to gather some
information. You will need (1) your final drive ratio,
also known as the rear end ratio; (2) the ratios of your
transmission gears; and (3) the effective radius of the
driven tire. The first two chunks of data you can usually
get from any service manual. The third one, effective
radius, you will need to measure because it varies from
one size of tire to another and even from one brand of
tire to another in the same size. Simply measure from the
ground up to the exact center of the wheel. Your tape
measure will have it in fractions, so you will need to
convert the fraction to a decimal equivalent. No big
deal.
Now the calculations begin. You will need to figure
out the "revs per mile" of your tire. Do this
by doubling the effective radius and multiplying that
number by 3.1416 (You can use 3.14 if you are doing this
on stone tablets with a chisel because your calculator's
battery died. The difference will be insignificant.). The
resulting figure is the circumference of the tire, which
is also the number of inches your car travels for one
complete revolution of the tire. Since there are 63,360
inches in one mile, dividing 63,360 by the tire
circumference will give the "revs per mile"
figure. Hang on to this number because you will be using
it a lot.
The significance of this number is that if your tire
is turning that many revolutions in one minute (rpm's),
you are going 60 mph. Let's use my Sentra SE-R as an
example. The effective radius is 10.75 inches, so:
| |
10.75 x 2 |
= |
21.5 |
| |
21.5 x 3.1416 |
= |
67.54 |
| |
63,360 / 67.54 |
= |
938 |
Now all you have to do is figure out how fast the tire
is turning. This is where you need those gear ratios.
Calculate the overall ratio for the gear you are
interested in, or do them all. Multiply the transmission
ratio by the final drive ratio. I'll just do 5th gear in
the Sentra. Final drive ratio is 4.18 and 5th gear is
0.76, so
If I want to know how many rpm the engine will be
turning at 60 mph in 5th, I multiply the tire revs per
mile by the overall ratio:
(or approximately 3000 rpm)
But suppose you only know your engine rpm and you want
to figure out how fast you were going in a particular
gear. Say your speedo is broken (must be a roadster) but
you know you were cooking down this road the other night
at 6,000 rpm in 3rd gear. How fast was that?
Easy to do. Divide your engine rpm by the overall
ratio in that gear. This gives you the tire rpm. Using
the Sentra again, the overall ratio in 3rd gear is 5.39,
so
| |
6,000 / 5.39 |
= |
1,113 tire rpm |
Since 938 rpm would be 60 mph, you can see this is
cooking right along! To figure out how much, divide the
tire rpm by the revs per mile and multiply the result by
60. This will be the speed in miles per hour.
| |
1,113 / 938 |
= |
1.19 |
| |
1.19 x 60 |
= |
71.4 mph |
If all this was put into the form of a formula, it
would be
| |
(engine rpm /
overall ratio) |
|
|
| |
------------------------------------- |
x |
60 = mph |
| |
(63,360 / (radius
x 2 x 3.1416)) |
|
|
which certainly looks more impressive, but is more
difficult for most people to use. What we did was start
on the bottom right and work our way left, then up, then
right to get the result.
Now that wasn't so hard after all, was it?
|