Daredevils, engineers, and even specialized police units use mathematical equations to find information about how vehicles and other objects can become airborne, and how far they can travel through the air. Though it may seem complicated, it is easy to calculate the distance an object will travel off a ramp, how high it will go, or how fast it will need to be moving to travel a specific distance.
Things You'll Need
- Ruler or tape measure
- Scientific calculator
Calculate the slope. Take a level and place it on a portion of the sloped ramp. Raise one end off the ramp until it is level, maintaining contact with the ramp on the other end. Now take a ruler and form a right triangle with the level and the ramp. Measure the distance to the ramp from the end of the raised level. The length of the level will be your run; the height of the level will be your rise. Divide the rise by the run to find the slope's percent of grade. Write this number down as m=Rise/Run, where m is your slope's percent of grade.
Find the departure angle, or φ. This is simply a matter of entering your slope into your scientific calculator and finding the tangent. Typically, all you will need to do is enter the number "m" and press the 2nd button on the calculator, then press "TAN." This is your departure angle. Write this number down as n=φ with "n" being your tangent.
Find the cosine and sine of of your departure angle (φ). Enter your tangent and press the 2nd button, then the "COS" button to find the cosine. Write this down as Cosφ and the answer. Then enter your tangent, press the 2nd button, and then the "Sin" button. Write this down as Sinφ and the answer.
Determine how fast you will need to travel to jump a known distance. Determine if the object you are launching off the ramp will land at the same height from which it took off, or higher or lower. Show this value as "h." The "h" is positive if the object will land lower than it took off and negative if it will land higher. Show the distance to be traveled as "d"' Find the speed required by multiplying Cosφ by the square root of "h" plus the absolute value of "d" times "m." Divide this value by the number you find from multiplying distance ("d") by 2.73.
Find the maximum height the object will reach if it leaves the ramp at a known speed by finding the velocity. Velocity is expressed in feet per second, or fps. To find the velocity, multiply the speed by 1.466. Multiply the velocity by Sinφ and square this value. Divide that number by 64.4, which is twice the rate of gravity.
Determine the distance the vehicle will travel, multiply the velocity squared by Sinφ and then multiply that number by Cosφ. Divide this number by the rate of gravity, or "g," which is 32.2.
- Photo Credit Jupiterimages/Brand X Pictures/Getty Images