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5 math formulas car nuts can actually use
Math is far from the most popular subject for many car folks. Who wants to be scribbling when you could be driving? The reality is, though, that there are a few formulas that come in handy. You might not even realize you know some of them, simply because you rarely write them out. We won’t demand you show your work, but here are a few formulas that just might help you on your next project.
You hear these numbers thrown around a lot in conversation, especially in the domain of performance vehicles. The final drive ratio describes the relationship between the number of turns of the input (the driveshaft) and the output (the axle/s). A simple example is 3:1, where for each three turns of the driveshaft the driven axle(s) spins once. Place a mark on the input to the differential and rotate the wheel one revolution, counting the times the mark on the input completes a full turn. Other common examples are 4.10:1, 3.55:1, or 2.73:1.
It’s tempting to finish up a V-8 engine swap by tightening down your favorite brand’s 850-cfm double pumper, but the fact is, carburetor size matters. The cubic-feet-per-minute rating on a carburetor signifies the flow capability of said air-and-fuel mixing device, and when properly matched up with your engine you will be rewarded with peak efficiency and horsepower. (Or you can elect for retrofit fuel injection, but what fun is that?)
Calculate the cfm requirements of your engine with this formula: cfm = (cubic inches x rpm x volumetric efficiency) ÷ 3456. For reference, most stock engines have a volumetric efficiency of roughly 80 percent. Warmed-over street engines will be roughly 85, and all-out race engines can be 95 percent or better. Don’t be surprised when the final number out of this math problem is a lot lower than you expect (or want) it to be. Be honest, and be sure about the maximum rpm your engine is built to handle.
When you refer to an engine by a number (the Chevy 350, or Ford’s 5.0), you’re naming it not by configuration (V-8, inline-four, straight-six) but by displacement. In terms of piston engines, rather than their rotary combustion counterparts, that is calculated in bore (or diameter of the cylinder) multiplied by the stroke (the piston’s vertical movement in the cylinder as measured at the piston’s dead center), with a little pi thrown in for good measure. Most of the time the factory kindly figures this out for us, but if you bore out an engine’s cylinders or swaps crankshafts you’ll need to crunch the numbers to find the exact displacement. Here’s the formula written out: displacement = stroke x 3.14 x (0.5 x bore)2 x number of cylinders.
Keeping your car from burning to the ground from an overloaded electrical circuit is quite simple using Watt’s law. Specifically, this formula reads as follows: power (in watts) = voltage x current (in amps). You can divide the wattage draw of the device you are wiring in by the voltage of you system and the answer is the fuse size you will need… kind of.
That is the exact current draw, meaning that if you install a fuse that exactly matches your math it will likely blow under regular use. Add 20 percent to that final figure and that will protect the system while also allowing current flow under normal operation. When calculating, be sure to use operating voltage, which can be over 13 volts even in a 12V system.
Many classic cars are equipped with basic gauge clusters, and if the original owner didn’t spring for the tachometer (assuming there was the option to spec one) you may have no idea how fast your engine is turning while cruising down the road. Sounds like it’s spinning mighty fast, doesn’t it? Without overdrive, many vintage engines spin higher at rpm than their modern counterparts, but here’s how you can be sure of the numbers.
Find out just how high your engine is spinning at a given speed with this formula: rpm = (mph x gear ratio x 336) ÷ tire diameter in inches. Calculate your gear ratio with the above formula, and then be sure to get the accurate rolling diameter by marking the tire and the ground with chalk and then pushing the car one tire rotation forward. Measure between the initial chalk mark on the ground and where the chalk mark on the tire completed one rotation. Divide that linear measurement by 3.14 to get the final rolling diameter. This also assumes a final drive of 1:1 for the transmission gear, which is the common top gear in many vintage transmissions.
Do any of these formulas clear up one of your automotive conundrums? Let us know below.