# How to calculate the energy lost in a projectile from drag?

• Necm
In summary, the problem at hand involves calculating the energy lost due to drag for a projectile being shot straight upwards. The force of drag is proportional to velocity, and the projectile's velocity is not constant. The suggested method is to use the potential energy difference between the maximum height with and without drag. This type of problem is often simulated in small time steps, taking into account the object's orientation and aerodynamic rotational forces.
Necm
The force of drag is proportional to velocity, but with a projectile velocity isn't constant, so how could i calculate the energy lost due to drag?
The projectile in question is being shot straight upwards, so that may make this problem much more simple.

Is this an actual experiment, where you will be measuring things like velocity, or is it a theoretical exercise where you will be given values for certain quantities?

Necm said:
The force of drag is proportional to velocity, but with a projectile velocity isn't constant, so how could i calculate the energy lost due to drag?
The projectile in question is being shot straight upwards, so that may make this problem much more simple.
Well, the energy lost is force times distance and the force of drag is a square function of velocity. You should be able to put that together (with, in this case, gravity) to find the energy loss due to drag.

You could use the potential energy difference corresponding to the maximum height you'd expect without drag and the maximum height with drag.

These problems are usually simulated in small time steps. At each time step, the object velocity and orientation is known and the resultant drag force is calculated. If the object is a sphere, you don't have to worry about its orientation. Otherwise, you need to also calculate aerodynamic rotational forces and keep track at each step of its orientation and resultant coefficient of drag.

## 1. How is drag force calculated?

The drag force on a projectile can be calculated using the equation Fd = 1/2 * ρ * v2 * Cd * A, where ρ is the density of the fluid through which the projectile is moving, v is the velocity of the projectile, Cd is the drag coefficient, and A is the cross-sectional area of the projectile.

## 2. What is the formula for calculating energy lost due to drag?

The formula for calculating the energy lost due to drag is E = Fd * d, where Fd is the drag force and d is the distance travelled by the projectile.

## 3. How does air density affect energy lost in a projectile?

As air density increases, the drag force also increases, resulting in a greater amount of energy being lost by the projectile. This is because the projectile has to push through more air molecules, creating more resistance and slowing it down.

## 4. What factors affect the drag coefficient of a projectile?

The drag coefficient of a projectile is affected by its shape, surface texture, and the properties of the fluid through which it is moving (such as air density and viscosity). The angle of attack and speed of the projectile also play a role in determining the drag coefficient.

## 5. Can the energy lost due to drag be minimized?

Yes, the energy lost due to drag can be minimized by using streamlined shapes, smooth surface textures, and reducing the speed and angle of attack of the projectile. Additionally, using materials with low density and high strength can also help to reduce the energy lost in a projectile due to drag.

• Mechanics
Replies
3
Views
5K
• Mechanics
Replies
8
Views
2K
• Mechanics
Replies
4
Views
792
• Mechanics
Replies
11
Views
1K
• Mechanics
Replies
5
Views
1K
• Mechanics
Replies
9
Views
2K
• Mechanics
Replies
5
Views
6K
• Mechanics
Replies
17
Views
17K
• Mechanics
Replies
13
Views
1K
• Mechanics
Replies
11
Views
2K