Aldo, at the Loose Change forums, is having trouble understanding the first error in Balsamo's article:
We are calculating vertical height for a 1.3 second duration. a.k.a distance, here. Not vertical acceleration/velocity. The vertical accelration is 75 fps. The G's needed to arrest a vertical height of 97.5 over a 1.3 second time interval based on 75 fps descent rate is 4 G's. If we need to arrest 75 feet in one second, how do you figure that height gets lower at 1.3 seconds? You just lowered vertical velocity to 57.7 when 75 is required.
Let's take this a step at a time.
We are calculating vertical height for a 1.3 second duration. a.k.a distance, here.
No you're not, you're calculating a value that you then divide by an acceleration (g, which is 32 feet per second per second) to produce an acceleration ratio (the "G" force, which is simply the ratio of an acceleration to g). So, you'd better be calculating an acceleration, or you're doomed from the start.
Not vertical acceleration/velocity.
Not vertical velocity, yes vertical acceleration. (Two different things! Keep them straight or you're lost!)
The vertical accelration is 75 fps.
No, the initial vertical velocity (rate of descent) is 75 fps. Accelerations cannot be measured in fps, you need fps per second, that is feet per second per second.
The G's needed to arrest a vertical height of 97.5 over a 1.3 second time interval based on 75 fps descent rate is 4 G's.
You're not arresting a height, you're arresting a velocity, within certain constraints of time and of distance descended in the process. It turns out the distance is a more stringent constraint than the time, but Rob started with the time in his analysis and I followed his same procedure (while correcting the math along the way).
Once you know that distance travelled is the limiting factor, you can do this in one step. Suppose you're in a car going 75 fps and you need to stop in no more than 40 feet of travel. What must your deceleration (that is, the magnitude of your acceleration in the direction opposite to the direction you're traveling) be? The formula is a = v(initial)^2 / (2 * d).
75 feet/second * 75 feet/second / (40 feet * 2)
= 70.3 feet/second-second
= 2.2 g (70.3 / 32)
Now suppose you're in a plane descending 75 fps and you need to level off with no more than 40 feet of additional descent from your current height. What must your upward acceleration be? Exactly the same problem, exactly the same answer.
If we need to arrest 75 feet in one second,
No. We need to reduce a descent rate (vertical velocity) of 75 feet per second, to a descent rate of 0 feet per second. That's what arresting the vertical velocity means. We have 1.3 seconds to do it in. (And also constraints on the distance we can descend in the process, but that gets taken into account in a later step.)
how do you figure that height gets lower at 1.3 seconds?
The plane is descending, is it not? Height gets lower over time, that's the definition of descending. But I don't think that's what you meant.
You just lowered vertical velocity to 57.7 when 75 is required.
No, I lowered vertical acceleration to 57.7 feet per second per second, in order to reduce a velocity of 75 feet per second to a velocity of 0 feet per second, in 1.3 seconds.
75 / 1.3 = 57.7 fps per second (75 fps change, in 1.3 seconds).
Correct.
"75 Feet Per SECOND change in 1.3 seconds" is less than 75 Feet per SECOND??
No, 75 feet per second change in velocity in 1.3 seconds (an acceleration of 57.7 feet per second per second) is slower (less acceleration) than 75 feet per second change in 1 second (an acceleration of 75 feet per second per second). It has .3 seconds longer to happen, so it happens slower.
You have 75 hamburgers to fry.
If you fry 57.7 hamburgers per hour,
you'll fry 75 hamburgers in 1.3 hours.
You have 75 fps of vertical velocity to arrest (reduce to 0 fps).
If you arrest 57.7 fps of vertical velocity per second,
you'll arrest 75 fps of vertical velocity in 1.3 seconds.
So, the acceleration needed to arrest 75 fps of vertical velocity in 1.3 seconds, is 57.7 feet per second per second.
That's about 1.8 times the acceleration of gravity, which is 32 feet per second per second. (NOT "32 feet." NOT "32 feet per second.")
However, as calculated above, the height limit is the limiting constraint. So you have to accelerate upward at 2.2 g (pulling 3.2 Gs) to level off after only 40 feet of descent, and that will take less than the 1.3 seconds you have.
Thats stundielicious.
The guy is completely confused.
Indeed.
Respectfully,
Myriad