There has always been a lot of discussion in this Forum regarding the “top speed” of a given quad, or the effect on “top speed” that tire and gearing changes might have on a given quad.

The result of these “top speed” discussions has always been a great deal of seat-of-the pants speculation supported by very few facts (not to mention name-calling, quad-bashing, and ad hominem attacks).

In order to dispel some of the confusion surrounding this subject, this post will demonstrate, how with the use of simple elementary school mathematics, the theoretical top speed may be calculated if one knows a few basic technical facts about the quad in question.

For the purpose of illustration, I will use my Kawasaki Bayou 400 as the subject of this exercise. All relevant data used here has been pulled directly from the Bayou 400 owner’s manual. To make this exercise easy to follow, I will first describe in general terms the equation used to calculate speed, and the premise on which it is based.

To calculate the theoretical speed of any motor vehicle driven by a combination of gears and wheels, which transmit the rotary motion of the engine to the surface on which the vehicle rests, it is necessary to know the following things:

1). The number of engine revolutions per minute.
Variable name: Er

2). Primary gear reduction ratio – the number of gear teeth on the crankshaft vs. the number of gear teeth on the transmission input shaft.
Variable name: Pr

3). Secondary gear reduction ratio – in the case of the Bayou 400, the number of teeth on the shaft-drive input gears at the engine, and the number of teeth on the shaft-drive output gears at the differential.
Variable name: Sr

4). Selectable gear ratio – the number of teeth on the gear set that comprises 1st, 2nd, 3rd, 4th gear and reverse etc.
Variable name: Sg

5). The actual measured diameter of the tire, NOT the nominal diameter of the tire as printed on the sidewall.
Variable name: Td

Knowing these five bits of information, we can calculate the theoretical speed in any selectable gear, at any engine RPM, in four easy steps.

Step 1: We use engine RPM, Primary gear reduction ratio, Secondary gear reduction ratio, Selectable gear ratio, and the number of seconds in a minute to calculate the number of axle revolutions per second – Ar, which by definition is equal to the number of tire revolutions per second. The formula looks like this:

Er/(Pr*Sr*Sg)/60 = Ar

Plugging in the numbers for the Bayou 400 at 8000 RPM in 4th gear, we get:

Ar = 8000/((75/29)*((20/14)*(39/9))*(26/34))/60 = 10.890

Step 2: We use the constant Pi, the actual diameter of the tire in inches, and the number of inches in a foot to calculate the circumference of the tire in feet – Tc, which by definition is the distance the quad will travel in one revolution of the tire. The formula looks like this:

(Pi*Td)/12 = Tc

Plugging in the numbers for the 25x10x11 Goodyear Mudrunners on the back of my Bayou 400, we get:

Tc = (3,14159*24.25)/12 = 6.349

Step 3. We use the number of feet in a mile and the number of seconds in an hour to calculate the number of feet traveled per second at a speed of one mile per hour – Fs. The formula looks like this:

Fs = 5280/3600 = 1.467

Step 4. We use axle revolutions per second – Ar, circumference of the tire in feet – Tc, and feet traveled per second at a speed of one mile per hour – Fs, to yield the theoretical speed – Ts, at engine RPM Er, when in selectable gear Sg. The formula looks like this:

(Ar*Tc)/Fs = Ts

Plugging in the values we calculated for the Bayou 400 in the preceding three steps, we get:

Ts = (10.890*6.349)/1.467 = 47.14

The calculated theoretical speed of the Bayou 400 at 8000 RPM, in 4th gear, when running 24-1/4-inch tires, is 47.14 MPH. This jibes quite well with my actual experience with the Bayou 400.

While a spreadsheet like MS Excel will allow you a great deal of easy “what if…” calculations, it is still possible to do all of this math on nothing more complicated than a four-function calculator.

Using these simple formulas, and with access to the technical data regarding a given quads gear ratios (usually available in the owner’s manual), you will never again wonder, “How fast can it go?” You’ll always have the answer… at least on paper.

Army Man

All I have to say, is WOW, If that is elemtry math to you, I'd hate to see your high school math! WOW!

:)

-JaReD

I must have been sick that day.

LOL

Armyman,

Are you sure you are not just TreeFarmer incognito? (lol)

Your statement, "(not to mention name-calling, quad-bashing, and ad hominem attacks)" needs to be explained to the majority so that all understand ad hominen means biased, unsubstansiated predjudiced statements and attacks; this is not to imply that readers are simple or stupid, this is just a word not used much in our society.

Allow me to also add that top speed should be realized with this set of criteria:
1. Given riding environment and terrain. The top speed of any quad is limited by what we ride in; ie. one will be able to achieve a higher top speed in an open field than in the woods.
2. Rider experience and ability. One who has been riding longer than others will more than like be able to go faster than a "newbie."
3. Rider comfort level. NOBODY, and I repeat NOBODY should feel under compulsion to ride fast than they are comfortable. Even if one's quad can go 55mph, if the one piloting the quad feels comfortable at 40mph, that is where they should say top speed is.

Have fun ride safe. I've got my slide rule out trying your formulas. (lol)

My dog ate my homework

Its SO much easier just to look down at my speedometer,
Bill

Honda Hunter,

While I am flattered by your suggestion that I may be the inimitable Tree Farmer incognito, I assure you I am not he.

Your observation that no one should travel any faster than they are equipped to, or feel comfortable in doing, is a wise one.

My purpose in creating the post in the first place, was not to promote “top speed” as an end in itself. But rather was to provide a relatively simple method for allowing the perennial, rhetorical question, “How fast can she go?”, to be answered by anybody, who like Jethro Bodine of the Beverly Hillbillies, “had done grad-e-ated the sixth grade”. It also provides the “What if…” types with the means to determine what effect changing a front or rear sprocket will potentially have on the vehicles speed.

As a doctoral student you obviously recognized the relative obscurity of the Latin phrase “ad hominem”. I thank you for your kindness in taking the time to explain its meaning to our readership.

However, given the dumbed-down level of teaching that passes for “education” today, (e.g., the City of Pittsburgh spends over $9,000 per student to turn out kids who “done grad-e-ated” the 12th grade with less knowledge and ability than Jethro when he “done grad-e-ated” the 6th – but I digress), how will anyone ever expand their vocabulary if they are not from time to time exposed to, and challenged by, some of the more difficult words in the English language?

To paraphrase a character from a novel written by another 19th Century English author who came after G.G. Byron:

“Are there no dictionaries!? Are there no thesauruses!?”

And as Maria Theresa’s daughter is reputed to have said:

“Let them look it up!”

Army Man

How do you compensate for tires expanding then? I had some tires that would balloon when I got going fast enough.

But, if you have changed from your original tire diameter and not changed the speedo gearing, your speedo will no longer be accurate.

All that math stuff is just to much for my hillbilly country self.Like bill said.I will look at the speedometer.....BOB