Projectile Motion with Lift and Drag

In summary, to solve for the distance traveled of a projectile, you will need to isolate the initial movement in the x and y axes and take the sum of the forces in each axis. You can use a time-in-air formula and then solve the differential equations x'' + \frac{A}{m} x' = 0 and y'' - \frac{L}{m} x' + g = 0 to get the position of x and y as functions of time. From there, you can find the time at y = 0 and solve for x(t) to determine the distance traveled.
  • #1
Padj01
4
0
I need an equation to solve for the distance traveled of a projectile. The variables that I have are lift coefficient, drag coeficient, launch angle and initial velocity. Could someone please help me find the formula I need. Thank you.
 
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  • #2
First, isolate the initial movement in the x and y axes. For X, use cosine multiplied by the angle, and for Y, use sine multiplied by the angle. Then, take the sum of the forces in each axis.

X=(Forward{X} movement - drag {Coefficient*normal force})

Y=(Upward{Y} movement - gravity + lift {coefficient*normal force})

Then, you can use a time-in-air formula.
 
  • #3
Then, you can use a time-in-air formula.

You are a far ways aways from the end of the problem, at this stage it is certainly not obvious which ""time-in-air formula" you are talking about.

This is a tedious exercise in differential equations, solve these:

[tex] x'' + \frac{A}{m} x' = 0 [/tex]

[tex] y'' - \frac{L}{m} x' + g = 0 [/tex]

To get position x and y as functions of time. From here these, you can figure out how far things go (answer: find t @ y = 0 and solve for x(t).)
 

1. What is projectile motion with lift and drag?

Projectile motion with lift and drag is a type of motion in which an object is launched into the air at an angle and experiences both upward lift and downward drag forces as it travels through the air. This type of motion is commonly seen in sports such as football, baseball, and golf.

2. How is lift and drag different from other types of forces?

Lift and drag are unique types of forces that act on objects moving through a fluid, such as air. Lift is a force that acts perpendicular to the direction of motion and is responsible for keeping the object in the air. Drag is a force that acts opposite to the direction of motion and is responsible for slowing the object down.

3. What factors affect the lift and drag forces on a projectile?

The lift and drag forces on a projectile are affected by several factors, including the shape and size of the object, the speed at which it is moving, the density of the fluid it is traveling through, and the angle at which it is launched. These forces can also be influenced by external factors such as wind and air pressure.

4. How can the lift and drag forces be calculated in projectile motion?

The lift and drag forces on a projectile can be calculated using mathematical equations that take into account the factors mentioned above. These equations use variables such as the object's mass, velocity, and surface area to determine the magnitude and direction of the forces. Advanced computer simulations can also be used to accurately calculate these forces.

5. How does understanding projectile motion with lift and drag benefit science and technology?

Understanding projectile motion with lift and drag is important in various fields of science and technology, such as aerodynamics, ballistics, and sports. It allows scientists and engineers to design more efficient and accurate projectiles, such as rockets and missiles. It also helps in improving the performance of athletes and sports equipment, leading to better results in sports competitions.

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