SEOUL TRAIN'S

CAR MATH

Here you can find mathematical formulas that apply to cars, from engine size formulas to tire formulas.

Chose one below:

Calculating g (lateral acceleration)

Calculating actual mph after putting a different tire size

Calculating Actual mph and speed error

Conversion formulas

Engine Displacement formula

Estimating 1/4 mile ET and trap speed

Horsepower from Torque formula

Horsepower loss from elevation

Piston Speed formula

Tire Diameter formula

Torque from Horsepower formula

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Calculating g (lateral acceleration)

Ok, you put big tires, sway bars, gummy tires, lightened the car, and now what? How do you know if you car is handling better? You gut feeling can tell you a lot, but sometimes hard figures are more fun. Well, to calculate g force you will need: a car (duh), a buddy, a timer, a long measuring rule (for over 30 feet), a cone and a free, flat parking lot. You DO NOT need a cop seeing you do this. Place the cone on the ground, and start turning circles around the cone (the cone is your visual reference, but don't look AT IT, catch it with the corner of your eyes). Make the circles as tight as you can, and drive as fast as you can, without losing grip. Your buddy stays outside the car (no passengers here) with the timer, timing your laps and paying attention to the circle your car is making. It is important that he knows where the outer edge of you tires are, because you're gonna need the radius of your circle. After you think you got enough laps, or you wrecked your car (preferably not hitting your buddy), average your lap times, and have your buddy measure the radius of your circles. The more exact the better. After you done all this and you ran away from the cops or paid your bail (depends on how lucky you are), you can use this formula to calculate how many g's your car is pulling:

lateral acceleration = 1.227 x [ (lap radius in feet) / (lap time in seconds )² ]

So let's say I was turning 200 feet circles with my Accent, doing one lap every 17.7 seconds:

lateral acceleration = 1.227 x (200 / 17.7²)

lateral acceleration = 1.227 x (200 / 314.35)

lateral acceleration = 1.227 x 0.6362

lateral acceleration = 0.7806

That means my 2000 Accent GS pulls 0.78 g thru the turns.

Calculating Actual mph After Putting a Different Tire Size

If you change tire sizes in you car your new tire will have a different size diameter, and that will affect your indicated mph. Use this formula to calculate the actual mph after the new tires:

actual mph = [ (new tire diameter) / (old tire diameter) ] x (indicated mph)

Let's say I substitute the factory 175/70-13 tires in my Accent with 195/50-15 tires, and I'm seeing 70 mph on the speedo. Using the tire diameter formula, I find out that the 175/70-13 tires have a 22.64" diameter, while the 195/50-15 tires have a 22.68" diameter. What is my actual speed?

actual mph = (22.64 / 22.68) x 70

actual mph = 0.99823 x 70

actual mph = 69.87654

Which works out to a little less than 70 mph. As you can see the speed difference is not that great, so I can use 195/50-15 tires without affecting my speedometer too much.

Calculating Actual mph and speed error

If you drive an older car or has put different size tires on your car most likely your speedometer doesn't show the actual speed anymore, so go to a flat road, keep a steady speed (don't change for a mile) and count the seconds between mile markers. Use this formula to calculate actual mph:

actual mph = 3600 / (seconds per mile)

Let's say my old car tells me I'm doing 65 mph, but I ain't sure. I counted 63 seconds between miles:

actual mph = 3600 / 63

actual mph = 57.14

My car is actually going at 57 mph! I've been cheated of 8 mph, but I'm less likely to be pulled over for speeding :)

Now I can use this formula to calculate my speedometer error:

speed error % = { [ (actual mph) - (indicated mph) ] / (actual mph) } x 100

Let's use the formula to calculate my speedometer error:

speed error % = [ ( 57 - 65 ) / 57 ] x 100

speed error % = ( -8 / 57 ) x 100

speed error % = -0.140351 x 100

speed error % = -14.03

Which means I have negative 14% error on my speedometer.

Engine Displacement formula

The formula for calculating engine displacement (the size of your engine) in liters is:

displacement =  [(pi / 4)x(bore in centimeters)²x(stroke in centimeters)x(number of cylinders)] / 1000

pi = 3.1415927

The 2000 Accent GS engine has four cylinders, a 7.54 cm bore and a 8.35 cm stroke, its displacement is:

displacement = [(3.1415927 / 4) x (7.54²) x 8.35 x 4] / 1000

displacement = [0.7853981 x 56.85 x 8.35 x 4] / 1000

displacement = 1491.30 / 1000

displacement = 1.491

We can round this number to one decimal digit, and it gives us 1.5 liters, which means this engine is a 1.5 engine.

Estimating 1/4 mile ET and trap speed

To get a rough estimate (this formula will be a little optimistic) of how long a car will cover the 1/4 mile, use this formula:

ET = [ (weight of car) / (max hp) ] ^1/3 x 5.825

My 2000 Accent GS weighs roughly 2500 lbs with my fat ass in it and a full tank, and it makes a maximum of 92 hp, so the ET should be around:

ET = ( 2500 / 92) ^1/3 x 5.825

ET = 27.1739  ^1/3 x 5.825

ET = 3.006426 x 5.825

ET = 17.5124

So my 2000 Accent GS should run the 1/4 mile in 17.51 seconds, MSN Carpoint tested this car and they did the 1/4 mile in 17.7 seconds.

To calculate the trap speed for the 1/4 mile, use this formula:

mph = [ (max hp) / (weigh of car) ] ^1/3 x 234

Using the same car for the formula we get:

mph = ( 92 / 2500 ) ^1/3 x 234

mph = 0.0368 ^1/3 x 234

mph = 0.33262 x 234

mph = 77.83

My 2000 Accent GS should have a trap speed of 77.83 mph.

Just in case you don't believe these 1/4 mile formulas work, check these comparisons between 1/4 mile numbers from the formulas and from car magazines:

BMW M Roadster: formulas: 13.9 sec @ 97.9 mph, Road & Track (Sep 99): 13.7 sec @102.0 mph           1.43% 4.18%

Honda S 2000: formulas : 13.4 sec @ 101.6 mph, Road & Track (Sep 99): 14.0 sec @ 99.5 mph    4.31% 2.03%

Porsche Boxter: formulas: 14.3 sec @ 95.1 mph, Road & Track (Sep 99): 14.6 sec @ 94.0 mph 2.09% 1.15%

VW New Beetle 1.8T GLS: formulas: 15.9 sec @ 85.6 mph, Road & Track (Nov 99): 15.6 sec @ 89.0 mph  8.17% 3.97%

The differences between the formula numbers above are between 1.43% to 8.17%, so these formulas won't give you exact numbers, but will provide you with a general idea of how fast your car is on the 1/4 mile.

Horsepower from Torque formula

To get the horsepower (hp) figure for a known torque figure (lb-ft) at a specified rpm, use this formula:

horsepower = [ (rpm) x (torque) ] / 5252

If you get the 2000 Accent GS engine, which produces 97 lb-ft @ 4000 rpm, you can get the horsepower figure for 4000 rpm:

horsepower = (4000 x 97) / 5252

horsepower = 388000 /  5252

horsepower = 73.88

So, the 2000 Accent GS produces 74 hp @ 4000 rpm

Horsepower loss from elevation

Unless you have a turbo or supercharged engine, your car is gonna lose power the higher up you go.

To calculate how many horsepower your car would have at a certain altitude, use this formula:

 hp loss = [ (elevation in feet) / 1000 ] x 0.03 x (hp at sea level)

The maximum horsepower that manufacturers usually quote for their engines is at sea level, so use the figure on the formula.

Since Fort Irwin, where I live, is at 2350 feet high, and Hyundai tells me my car makes 92 hp at sea level, I have lost this many horsepower:

hp loss = ( 2350 / 1000) x 0.03 x 92

hp loss = 2.35 x 0.03 x 92

hp loss = 6.486

If I subtract 6.5 hp from 92 hp I can deduce that in Fort Irwin my car only makes 85.5 hp!

I can also deduce that I need a turbo.

Piston Speed formula

To calculate the speed, in feet per minute, at which your pistons are traveling, use this formula:

piston speed in fpm = [(stroke in inches)x(rpm)] / 6 

To convert your metric stroke (in cm) to inches, follow this formula:

inch = cm x 0.3937008

If the 2000 Accent GS engine has a 8.35 cm stroke has a rev limit of 6250 rpm, the piston speed at max rpm will be the following:

piston speed = [(8.35 x 0.3937008) x 6250] / 6

piston speed = [ 3.287 x 6250 ] / 6

piston speed = 20546.26 / 6

piston speed = 3424.37

So, on this engine with a 8.35 cm stroke, its piston will be traveling at 3424 feet per minute at 6250 rpm!

Tire Diameter Formula

To calculate the diameter of a metric size tire you need first to understand tire sizes: a 195/50-15 tire means that the section width (where it touches the road) of the is 195 mm, it has a 50% aspect ratio (the side walls are 50% as high as the section width is wide) and it fits a 15" wheel. Using this formula you can calculate the tire diameter:

tire diameter = 2 x { [ (section width) x (aspect ratio) ] / 2540 } + (wheel diameter)

Using that same 195/50-15 tire, we get:

tire diameter = 2 x { [ 195 x 50 ] / 2540 } + 15

tire diameter = 2 x (9750 / 2540) + 15

tire diameter = 2 x 3.83858 + 15

tire diameter = 7.67716 + 15

tire diameter = 22.67716

So a 195/50-15 tire has a 22.68" diameter.

Torque from Horsepower formula

Use this formula to get a torque (lb-ft) figure from a known horsepower (hp) at a specified rpm:

torque = [ 5252 x (horsepower) ] /  (rpm)

A 2000 Accent GS engine makes 92 hp @ 5500 rpm, so the torque at 5500 rpm is:

torque = ( 5252 x 92 ) / 5500

torque = 483184 / 5500

torque = 87.85

So a 2000 Accent GS engine makes 88 lb-ft @ 5500 rpm.

Conversion formulas

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