Car Jump Distance Calculator

The calculator was divided into three sections.

Jump parameters: 

That is the central section that must be completed in order to see any results. You must provide the following information:

• Slope and height of the take-off ramp – the slope should be expressed in angle units;
• Landing ramp height – if the landing ramp is too high for a jumping car, we only show the results for the first part of the jump;
• Take-off speed is the speed at which the car is travelling just before it takes off. 
• Standard gravity – we set it to 1 g by default, which is the average gravitational force on Earth. You can change it to the standard gravity of other planets or adjust it to the standard gravity of your location.

That's all you'll need to investigate a simple projectile motion problem. You'll need to enter more values for more advanced calculations. Choose whether you want to account for air drag, calculate car tilt during a jump, or do both. There should be a new section called "Advanced calculations."

Calculations that are more complex:

You must specify the car's mass, length, and height regardless of the advanced options you select. The former refers to a car's total mass, which includes all equipment, fuel, and the weight of its passengers. Furthermore, the air drag force option necessitates:

• The density of air is 1.225 kg/m3 under normal circumstances. To find the density of air for your specific jumping conditions, use our air density calculator.
•  Automobile drag coefficient – you can verify the drag coefficient for various cars here.

Additional parameters are required for the car tilt calculation:

• The distance between the rear and front axles of a car is referred to as the wheelbase.
• The longitudinal and altitudinal positions of the centre of mass, which you can estimate using our car centre of the mass calculator.
• Car height – the car height is needed to estimate the moment of inertia (if you don't know how much it weighs) and air resistance; and
• Moment of inertia – if you understand the precise value of the moment of inertia, you can type it directly into the field. This moment of inertia revolves around the axis that runs parallel to the car's width and passes through the car's centre of mass. To learn how we calculate the approximate solution of mass moment of inertia in the car jump distance calculator.

The car jump distance calculator's chart allows you to select one of the physical parameters that change during the jump. The values with the x and y subscripts should be obvious – they are positions, velocities, and accelerations measured in a specific direction. The following are the meanings of the remaining parameters that do not have subscripts:

• Distance d = √(x² + y²);
• Total velocity |v| = √(vx² + vy²);
• Total acceleration |a| = √(ax² + ay²); and
• Tilt angle θ = the car's angle with respect to the horizontal line

Get similar concepts of physics all under one roof explained clearly with step by step process on Physicscalculatorpro.com a trusted portal for all your needs.

We model the car in our calculator as a solid rectangular prism with a constant density and a rotation axis passing through one of its sides (width). For the solid cuboid moment on inertia, we start with the following:

Icm = 1/12 * m * (l2 + h2), 

Icm = the moment of inertia of a solid cuboid rotating about an axis parallel to the cuboid's width and passing through its centre of mass; 

m = mass

I = denotes a cuboid length

h = cuboid height.

The formula must be revised because the car's centre of mass does not lie in the centre of the cuboid. We did it by adding up the moments of inertia of four smaller cuboid boxes, yielding the following formula:

Icm = 1/3 * m * [h2 + l2 - 3 * h1 * (h - h1) - 3 * l1 * (l - l1)],

Where, h1 and l1 are the height and length of the centre of mass, respectively (check the first section for a picture).

I = Icm + m * d2,

where I is the moment of inertia about an axis that is parallel to the first axis but offset by d.

1. What should I know before driving off a ramp in a car?

First and foremost, despite our best efforts, we are unable to perform precise calculations, which would necessitate modelling a specific car and specific jumping conditions.

Perform a few tests with small launching angles and start increasing the ramp angle before deciding to make a big jump. Also, keep in mind that a car would likely slow down on the ramp, resulting in shorter jumping distances. You don't want your hood to collide with the ramp's edge!

2. What does it mean when a car is tilted?

The instantaneous torque acting on the car's centre of mass causes it to rotate in mid-air. The car is aligned parallel to the horizontal axis when the angle is zero. The car's front endpoints up in negative angles and down in positive angles.

In polar coordinates, it's a common way to measure the angle. The zero point is on the right axis, 90 degrees is on the right axis, and so on.

3. How do you work out the height of a jump based on the force?

You can get the vertical displacement by calculating vertical acceleration from vertical force data; a=F/m, and then double-integrating the acceleration with time. Subtract the vertical displacement while standing from the highest vertical displacement to arrive at the jump height.