Date: Sun, 24 May 1998 00:32:29 CDT
Reply-To: Joel Walker <JWALKER@UA1VM.UA.EDU>
Sender: Vanagon Mailing List <Vanagon@vanagon.com>
From: Joel Walker <JWALKER@UA1VM.UA.EDU>
Subject: calculating speed from rpm
Content-Type: TEXT/PLAIN; charset=US-ASCII
one of the list members and i were chatting about this, and i typed up the
article i'd used before to calculate speeds at certain rpm in my buses.
i got to thinking that some of the rest of you might be calculator freaks :)
so here it is:
ok, here's the article from Road & Track (don't remember which issue):
Calculating rpm and speed
Question:
I'm interested in calculating how fast my engine will rev in every gear,
for a given speed, with different tires. Is there a formula relating
tire size, engine speed and road speed?
Answer:
the relationship between engine speed (rpm) and road speed (mph) is determined
by the characteristics of the drivetrain, from the crankshaft to the tire
contact patch. to calculate road speed for a given engine, you will need to
know the gear ratio(s) and the final drive ratio, or the overall ratio, and
the rolling circumference of the tires connected to the speedometer (usually
the driven tires).
the rolling circumference will be the most difficult to determine; gear ratios
can be found in your owner's manual or R&T data panel. to find the rolling
circumference directly by measurement, put a chalk mark on the tire and the
ground so that they line up. with the car loaded normally (say, half a tank
of fuel and the driver aboard), roll the car for exactly 10 revolutions of
the tire to average things out a bit. mark the ground again, lining up the
chalk mark on the tire. use a steel tape measure to find the distance covered.
alternatively, you can look up the circumference in the table below, which
lists some of the more popular tire sizes. this table was compiled from
tire-industry standards for the rolling circumference of new tires at
50 km/h (31 mph); the rolling circumference will vary from brand to brand,
with speed, load, inflation pressure and wear. even radials exhibit "growth"
at high speeds. error limits for the numbers in this table are +1.5 percent
and -2.5 percent.
as a last resort, you can estimate the rolling circumference from the
tire-size designation. for example, a 195/60R-15 tire will have a section
height of 60 percent of 195mm, or 117mm; in English units, 4.61 inches.
add to this one-half of the 15-in. wheel diameter, and you get 12.11 in.
multiply by 2pi gets the circumference using inch units; then dividing by
12 gets you to the circumference in feet.
the formula relating road speed and engine rpm is
mph = (rpm * cir) / (gear * final * 88)
where rpm = engine rpm
cir = tire cicumference, in feet
gear = gear ratio of your car
final = final drive ratio of your car
88 = combines several conversion factors
for example, the audi 90 quattro (R&T, december 1987). its tires are
195/60VR-14,so our calculated circumference works out to be 72.92 inches
or 6.08 feet. its final drive is 4.11:1, its 5th gear is 0.79:1, so their
product is 3.25 and the rest is a quick calculation away:
mph = (rpm * 6.08) / (3.25 * 88) = 0.0213 rpm
so, for instance, the audi will do 21.3 mph for every 1000 rpm in 5th gear.
to work the equation the other way, to find engine rpm for a given road speed,
you want to solve for rpm:
rpm = (mph * gear * final * 88) / circumference
at 60 mph, for instance, this has our audi revving a calculated 2822 rpm,
within a few percent of our road-test computer's 2750 rpm.
tire size circumference (feet)
185/60 R14 5.79
185/65 R14 5.97
185/70 R14 6.25
195/60 R14 5.91
195/65 R14 6.10
195/70 R14 6.36
205/55 R14 5.86
205/60 R14 6.02
205/70 R14 6.53
215/70 R14 6.66
------------------------------------------------end of article-------------
when i did mine, i did the 10x rolling tire chalk mark method, in a mall
parking lot. my 195/??R14 tires came out to 6.30 feet circumference, and
the bentley book provided the gear ratios:
reverse 3.67
1st 3.78
2nd 2.06
3rd 1.23
4th 0.83
final 4.86
and that's it. have fun. :)
joel
