Whether you realize it or not, math is a fundamental function of life and we use it on a daily basis. We use math for everything from balancing our checkbook, to computing fuel mileage, to purchasing aftermarket goodies, to counting the number of cars ahead of you at the stoplight. Even more impressive is that it's the only universal language in the world.
The point is, math is a precise, consistent, and invaluable tool for all gearheads when applied properly. We can use some simple math formulas to calculate relationships between tires and rpm for ideal gear ratios, compression ratios, the exact engine displacement with various bore and stroke combinations, and even to project quarter-mile and top-end speeds. Don't worry, we're not going to subject you to flashbacks of failing high school calculus. Instead, we're going to introduce some of the more basic car-guy formulas that only a true gearhead can appreciate. This won't be painful, and it just might be fun.
Horsepower & Torque
If you know either the horsepower or torque figures at a given rpm, it's easy to calculate the missing figure by simply plugging in the numbers.
Torque x RPM / 5,252 = Horsepower
415 x 4,000 / 5,252 = 316
Horsepower x 5,252 / RPM = Torque
316 x 5,252 / 4,000 = 415
This example is taken directly from our Titan 351 Ford Windsor at 4,000 rpm.
Selecting a Carburetor
Gearheads generally tend to over-carburete most engine combinations. Hey, we're just as guilty, but here's a simple formula that'll help make the selection process a little easier. Keep in mind that all combinations will vary, and this is only to help get you started. For mild street cars, take the maximum rpm and multiply it by the engine displacement. Next divide that number by 3,456 and multiply it by 0.85. For more dragstrip-oriented vehicle, replace the 0.85 constant with 1.1.
For example, if you plug in a maximum 6,000 rpm and a 350ci displacement, you end up with 516 cfm for the mild combo, and 670 cfm for the higher-horsepower version. These are just estimates, but it does offer suggestions on carburetor sizing if you're just getting started.
Street 350 ci
6,000 rpm x 350 / 3,456 x 0.85 = 516 cfm
Stroker 410 ci
7,000 rpm x 410 / 3,456 x 1.1 = 914 cfm
Compression Made Easy
If you enjoy experimenting with engine combinations and have access to the Internet, be sure to log onto www.performancetrends.com. Performance Trends offers an array of downloadable demo programs with enough visual effects to keep you entertained for hours. Our personal favorite is the compression-ratio calculator. This simple program allows you to calculate the compression ratio, cylinder-head volume, and engine displacement through a variety of inputs. It also allows you to determine the effects of various bore-and-stroke and rod-to-stroke combinations, figure out both cranking compression pressure and the dynamic compression ratio, and determine piston dome or dish volume. Pretty sweet, eh?
To calculate cubic-inch displacement, you'll need to know the bore and stroke of the engine, the number of cylinders, and the handy constant of 0.7854, which is shortcut representing a portion of the volume equation of a cylinder-3.1417 (pi) divided by 4. Then just plug these numbers into the equation below. For example, to find the displacement of a 350ci small-block Chevy with a 4.00-inch bore and 3.48-inch stroke, merely multiply bore times bore times stroke times 0.7854 times the number of cylinders-easy, no?
Displacement = bore x bore x stroke x 0.7854 x number of cylinders
Displacement = 4.00 x 4.00 x 3.48 x 0.7854 x 8 = 349.84 ci
If we wanted to build a 383 stroker out of a small-block Chevy 350, it's easily done with either a standard 4.00-inch bore block or even with a 0.030-overbored block. The standard block would require a 3.80-inch stroke, while the 0.030-overbored block would need a 3.75-inch stroke. Both combinations are really 382s, and if you absolutely had to have the stroker design closest to 383 ci, the overbore block is slightly closer at 382.7 ci. See for yourself.
4.00-inch bore 383
4.00 x 4.00 x 3.80 x 0.7854 x 8 = 382 ci
4.030-inch bore 383
4.03 x 4.03 x 3.75 0.7854 x 8 = 382.7 ci CC
Tire Diameter and Gear Ratio
Big tires may be cool, but swapping taller or shorter tires will affect the final drive ratio. Taller tires effectively change the rear gear ratio, making it "taller" or numerically less. Shorter tires create the opposite effect.
Image you're building a Pro Street show car, and the 9-inch is already set up with 3.08 gears based on a typical 26-inch-tall tire. Obviously, the car will look killer with a set of monster 33-inch-tall Mickey Thompson tires, but this swap to the much taller tires instantly transforms the final drive ratio from 3.08 to 2.42! The high gearing is great for the likes of Silver State runners but will be absolutely horrendous for this big-tire street cruiser. Of course this is a rather extreme example, but nevertheless you get the idea. To calculate your own configurations, simply take the current tire diameter and divide it by the new (taller) tire and multiply that by the current gearing.
Effective Gear Ratio = (original tire diameter / new tire diameter) x gear ratio
Effective Gear Ratio = 26 / 33 x 3.08 = 2.42