# Why Is a 200 lb Object Falling 200 ft Only Reaching ~23 m/s?

• Kamiden
In summary, the conversation is about a programming project to calculate Newtons of impact force from a fall, taking into account factors such as weight, air resistance, and density of the landing surface. The main issue being discussed is how to determine the area of a human in various free-falling positions, with suggestions to research skydiving/parachuting for estimates. The conversation concludes with a mention of needing to know the spring constant of the landing surface to convert impact speed to force.
Kamiden

## Homework Statement

1. I'm trying to write a program to calculate Newtons of impact force from a fall given the weight, general size, shape, and density of an object. I want to take air resistance into account. I also want to take the density of the thing the object falls on into account. I am having trouble figuring out why a 200 lb object falling 200 ft is going ~23 m/s at the point of impact. This is the loop I am using.

2. For reference:
3. accel = acceleration, which is set to 9.81 m/s^2 originally.
4. densitya = density of air, set to 1.2754 kg/m^3
5. drag = drag coefficient, set to .6 for the shape.
6. area = area of the object, set at .58 m^3
7. dragf = drag force in Newtons
8. weight = weight. Mass in kg * 9.81
9. mass = mass in kg, 90.7185
10. rheight = remaining height. This is in meters, and is set to 60.96

11. while (rheight > 0)
12. {
13. time = time + 0.01;
14. velocity = velocity + (accel*.01);
15. dragf = ((densitya*drag*area)/2)*(velocity*velocity);
16. accel = (weight - dragf)/mass;
17. rheight = rheight - (velocity*.01);
18. }
19. cout << velocity << " " << time;

20. Am I getting a formula wrong, is the code bugged, or is it something else?

## Homework Equations

Drag Force = (p*Cd*A)/2*v^2
Velocity = d/t
Weight = m * 9.81
Acceleration = W - Df

## The Attempt at a Solution

Seen above.

Last edited:
I think I found your error in line 19. It should read rheight=rheight-velocity*.01. A first test of the program would be to try setting the drag force equal to zero and see if you get a good answer.

Thank you. That was causing error, but now I am having a different problem. I have no idea what to use for area. Equations for shapes are easy, but what about for a human in various positions free-falling? (It's a fall damage calculator for a game)

The main ones I'd need to know is kneeling position, prone, and swan dive.

Kamiden said:
Thank you. That was causing error, but now I am having a different problem. I have no idea what to use for area. Equations for shapes are easy, but what about for a human in various positions free-falling? (It's a fall damage calculator for a game)

The main ones I'd need to know is kneeling position, prone, and swan dive.
Try reading about skydiving/parachuting. I think with arms spread out, etc., a free fall reaches a limiting velocity of about 100 m.p.h. , but if you google it, you might find the info you need.

I tried that. I tried that a lot. The best I get is to find the cross-sectional area. I have no idea how to find the area on a freeform object. Would that just be looking from directly below?

Could I use paint and pixels to feet as a proportion?

Kamiden said:
I tried that. I tried that a lot. The best I get is to find the cross-sectional area. I have no idea how to find the area on a freeform object. Would that just be looking from directly below?

Could I use paint and pixels to feet as a proportion?
Projected area would give a suitable estimate. I do think any kind of free fall estimates through the atmosphere is a rather inexact science.

Estimates are fine as long as they're at least mostly realistic in this case. Thank you for your help. I got it from here.

To convert impact speed to force you would need to know the spring constant of the landing surface.

## 1. What is fall velocity?

Fall velocity, also known as terminal velocity, is the maximum speed that an object can reach when falling through a fluid, such as air or water. It is the point at which the drag force of the fluid equals the gravitational force on the object, resulting in no further acceleration.

## 2. How is fall velocity calculated?

The fall velocity of an object can be calculated using the following formula: V = √(2mg/ρACD), where V is the fall velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and CD is the drag coefficient.

## 3. What factors affect fall velocity?

The fall velocity of an object can be affected by several factors, including the mass and size of the object, the density and viscosity of the fluid, and the shape and surface texture of the object. Other factors such as altitude, air pressure, and wind can also have an impact on fall velocity.

## 4. Why does the fall velocity of different objects vary?

The fall velocity of an object can vary depending on its physical characteristics, such as mass, size, and shape, which affect its drag coefficient. Objects with a larger surface area or a more streamlined shape will experience more air resistance and therefore have a lower fall velocity compared to objects with a smaller surface area or a less aerodynamic shape.

## 5. What is the strange answer to fall velocity?

The strange answer to fall velocity refers to the fact that, contrary to popular belief, the fall velocity of an object does not continue to increase indefinitely as it falls. Instead, it reaches a point of equilibrium when the drag force equals the gravitational force, resulting in a constant fall velocity. This strange answer can be explained by the principles of fluid dynamics and the laws of motion.

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