How to estimate RPMs per given speed.

[ricksmol]

This might get a little confusing.

When trying to calculate the RPMs of a motor at a certain speed, one of the factors required is the diameter of the wheel of the automobile.

This is to ascertain how many (miles/feet/inches etc) the car will move forward with each complete turn of the wheel.

Circumference= PI*diameter


If you measure the diameter of a wheel when not under the load of a car you might measure let us say 24.5 inches.

therefore circumference = 3.14*24.5= 76.93 inches. In other words the car will move forward 76.93 inches with each turn of the wheel.

However in real road conditions the tire is compressed by the load of the car. This compression remains constant throughout the complete turn of the wheel.

You might measure a diameter of 23.5 inches for a compressed wheel.

circumference= 3.14* 23.5= 73.79 inches of forward movement.

This would mean that at 2000 RPM there is a difference of

(2000*76.93)-(2000*73.79)=6,480 inches/min or 540 feet per minute or 32400 ft/hr. Which is the equivalent of about 6 MPH.


Now which is the correct way to estimate RPM? Any ideas.

Rick

 

[addo]

This is XECUTE's territory.

 

[StrangeRanger]

Deflection under load is a static condition. The problem is that there are some dynamic factors involved which can vary with speed and acceleration. As you spin the tire, its diameter increases slightly due to inertia and the tread patch tends to roll up on top of itself (very noticable in a top fuel car, but present to a lesser degree in normal tires.) As a result there is no really accurate way. Most tire manufacturers publish revs/mile data for their tires which you can look up on their web sites or at the Tire Rack. If you just want to be in the ballpark try taking the calculated tire diameter and subtracting about 3/4" to 1" and calculating revs/mile from that. You'll be close

 

[Silver Shadow]

I know thet it is past my bed time and I'm tired and probably missed it. But don't you need to know the gear ratio to figuar this thing back this way?

 

[Anonymous]

www.thirdgen.org/newdesign/tech/calculations.shtml

 

[ricksmol]

3pennyford:
I am assuming a 1:1 gear ratio for comparison purposes.

Chevytown:

That is a good calculator but it still doesn't solve my problem. And this is strictly theoretical but an inch in difference in the diameter of the tire makes a difference of 6 miles of traveled distance in one hour at a given constant RPM.
Rick
PS I live east of east L.A.... El barrio fuera del barrio.

Rick

 

[Anonymous]

Montebello?

 

[xctasy]

Here's my approach...which is of course, not like anyone elses There are three sides to your question. The first is "what the heck is the difference in rpm between a given tire size. The second is "how the heck do I calculate rpm with my tire size". The third is "for any given mph that I chose, what is the rpm?"

The first part first.

Equation (or principle) 1: The difference in speed and rpm is proportional to the diameter difference in the tire.

So if you've got 60 mph at 2000 rpm with a 24.5 " tire.

Therefore what the heck is the rpm at 60 mph with a 23.5 " tire : .

Answer: for a 23.5 " tire to do 60 mph the rpm increase is (24.5/23.5)*2000 rpm, or 2085 rpm. Difference in rpm is 85 rpm more.

Maybee you go for a new 215/65 15 tire, which is 25.5 loaded brand spankers with a full new tread. If the wheel was brand new, with half an inch of tread right the way round the circumference of the tire, there would be an extra inch of diameter, it may have 25.5 " inches of diameter rather than, say 24.5 by the end of its life". Then what would the rpm be?

Answer:for a 25.5 " tire to do 60 mph the rpm increase is (24.5/25.5)*2000 rpm, or 1922 rpm. Difference in rpm of 78 less.

Note you always use the standard tire your comparing as the numerator, and divide the size your proposing as the denominator.

There is a mathematically correct way of assessing the situation by algebra but it's all too hard for me.

The second answer to what is the rpm at a give speed, is to

Equation 2: take the static unloaded diameter, multiply it by 2.911 , then divide by the diff ratio. [Note that the value 2.911 becomes 2.975 if you've measured the loaded radius]

.

This the mph per 1000 rpm for a given tire in a 1:1 top gear. (for a 3000 pound car on a radial). For 2000 rpm, multiply by two, for 5000 rpm multiply by 5.

Example 1: Say you car has an overall top gear of 0.77 :1 in 5th, and a diff ratio of 3.22:1, tires 24.5 inches unloaded. The the mph per 1000 rpm is (24.5*2.911)/(3.22*0.77) = 28.77 mph per 1000 rpm.

Example 2: Say you've got a 23.5 loaded wheel, a 2.77:1 diff, and a 1:1 top gear. The the mph per 1000 rpm is (23.5*2.975)/(2.77*1.0) = 25.24 mph per 1000 rpm.


* For most cars, the static unloaded diameter verses the loaded moving diameter (the net crush) is 2.2% of the total tire diameter. This only happens at the bottom of the tire.

Now than answer to your question.

Equation 3: Since your trying to find two varaibles, you need to use a simultanoeus equation, or just work out equation 2, then divide the speed you want by the solution to what the mph per 1000 rpm is.

So for an Example 1 car doing 60 mph, the rpm is 60/28.77 = 2.086 , which should be multiplied by 1000 to get rpm. 2086 rpm. Example 2 car doing 60 mph is (60/25.24)*1000 = 2377 rpm.


As easy as A-C-B. Or something like dat

 

[Anonymous]

Make sure to have the proper pressure (iirc the pressure on the side is cold pressure) then warm them up with a cruise on the highway. Them measure from the center of the wheel hub to the ground, as it sits on the vehicle. That is the effective radius. Use that to compute the effective circumference and from there the actual mph.


-=Whittey=-

 

[ricksmol]

Chevytown:
Hacienda Heights.


Execute:
I'll have to chew on that for a while

Whitey:
What you state above makes a lot of sense as a useful tire measurament.

Rick

 

[Anonymous]

i made up a spreadsheet that can figure MPH, RPM, Gear Ratio and Tire Diameter; if you are trying to find one, you need to know the other 3 numbers

http://members.cox.net/gork1/Formulas.xls

and no there are no viruses in the file

make sure that when you do the gear ratio part that you multiply the transmission gear ratio times the final ratio