And to calculate the approximate distance, take half the terminal velocity and multiply by the time. As @BlackTalon noted, this is all pretty approximate, not only because the parameters are estimates, but also because the time calculation neglects drag.
drag is part of calculating the terminal velocity, so it's in there.
An Omega SMP300 would do really well at these tests as long as the helium hadn't leaked out of the valve.
Maybe Adrian Newey could design the next phone so that no matter how you drop it, it never travels fast enough to break.
It's ok to do that as a rough approximation, but obviously if you want to be accurate, you can't use drag to calculate the steady state velocity but then neglect drag when calculating the amount of time required to reach that velocity.
Ah, theory vs practice. You are correct, Professor. In practice, the factor of safety covers it
But then to calculate the time required to reach terminal velocity, you simply assumed constant acceleration, i.e. a linear increase in velocity versus time. That's incorrect because it neglects drag, which increases approximately quadratically with velocity.
Ah, theory vs practice. You are correct, Professor. In practice, the factor of safety covers it
I am an applied math professor and agree 100% with Dan here:
I would also add that the question of how long it takes to reach terminal velocity is ill defined, because terminal velocity is an asymptotic state. You never truly reach terminal velocity. If I make an incorrect assumption for mathematical convenience that drag is linearly related to velocity, and not quadratically, the velocity becomes
v(t)=v_T e^(-( 9.81/v_T) t) - 9.81
where v_T is the terminal velocity in meters/sec. The graphs of v(t) vs. t are shown below for v_T = 54 and v_T=89. As you can see it takes a fair bit longer to get close to terminal velocity than the rough approximation v_T/9.81. The velocities are negative because the height is decreasing.
I'm tempted to get out a DE solver for quadratic drag, but I think it is better for me to prepare for classes that start next week.
Not sure what this means, engineers need to have the mathematical abilities to make accurate and practical real-world calculations.
