Hey, I was just going to Private message this, but I dont think the forums supports it, or i couldn't find it. Sorry.
"But wait! We said earlier that the velocity of an object in free fall at any given
time is equal to gravity*time, so lets substitute that in!
Ft = mg-(1/2)pAC(gt)^2" - Shalmezad
I was reading your article, good Idea. However the above statement does not work.
It's true in a free fall, the velocity of an object is based on time. However, in a wind resistant
enviroment, this isn't accually true. In the end your calculating force of wind resistance based
on constant acceleration. I appreciate your desire to simplify variables, but it doesnt work.
Whats the Wind resistance at say 5 seconds, 10 seconds. 100 seconds?
As proof, I will plot some points of your formula.
Mass(m) 100KG - Fat man like me :)
Gravity(g) -9.81m/s^2
Desisty of air(p) 1.3kg/m^3
Cross Section(A) .75m^2
Coefficient of Drag(C) 0.5
Ft = mg-(1/2)pAC(gt)^2
A = (mg-(1/2)pAC(gt)^2)/m
Time: Ft: A: Direction of Acceleration:
0.0s 981N 9.81m/s^2 (Down)
1.0s 962.9N 9.63m/s^2 (Down)
5.0s 529.9N 5.30m/s^2 (Down)
7.0s 96.8N .968m/S^2 (Down)
7.5s -34N -.34m/s^2 (Up)
10s -823N -8.23m/s^2 (Up)
20s -6237N -62.4m/s^2 (up)
.
.
100s -179 461N -1795m/s^2
// Ouch
Thank you for pointing this out!
Sorry for my late response, I haven't been here in a while...
The key thing I would like to note again is the difference between acceleration and velocity, and once I re-explain, things should be clear.
Velocity of course, is how fast an object is going at any time.
Acceleration is your change in speed over time, this can also be renamed "the slope of the velocity graph"
When you are doing your calculations, you were calculating the acceleration. Yes, the acceleration ends up being a negative, and that's actually what is supposed to happen. It's going to be a little hard to explain, but it goes something like this:
When you are accelerating (your acceleration is positive), your "speed" is increasing (for now, I'm going to use the word speed, even though the correct term is velocity), so your speed will have a positive slope, but when you have a negative acceleration, your speed is decreasing, resulting in a negative slope.
Now when you do your calculations, you have to remember that when you switch to a negative acceleration, you already have a velocity, which means that instead of going up, you are slowing down, which is exactly what happens when you skydive.
When skydiving:
You speed up (Fg>Fa, your acceleration is +)
You reach a switch point (Point where your acceleration hits 0)
You slow down (Fa => Fg, your acceleration is -)
You reach terminal velocity (Fa=Fg, meaning that your acceleration is back to 0)
It's a good thing you pointed this out, because I should now mention that at the point where your Fa=Fg, whatever velocity you are going at is final, you neither speed up nor slow down. This is why I included everything needed to calculate these in my document.
Thank you for your concern, I should note however that there may still be errors in the document, so be sure to let me know if there are any other errors you come across.
-Richard
