Hm... as much as I know about math I know nothing about what kylekatarn just pointed out.

kylekatarn just quoted from a physics site ... if you really need the formulas, someone could dissect it all for you. But what I got out of that is that it does not matter what the mass of the halfling is.

As he or she falls the velocity keeps increasing until the downwards acceleration caused by gravity equals the drag caused by the air. That is why skydivers can fall faster when they "arrow" themselves, and they can slow up when they "spreadeagle" themselves (and they really slow up when they let the parachute open!).

So, I am afraid we are back to that windtunnel for tests. We will also have to ask your halfling to try different positions to see how that affects the drag, too.

]]>However I can tell you what a halfling is, think of a human being only 1/4th the size roughly... like a child that grows to be an adult in every way exept shorter life span and lacks the vertical height a human has. They are tricky little things. Read some TSR(Wizards books now) there are plenty of Halflings in those fantasy novels. Good books too.....]]>

One common model is that the resistance force is proportional to the speed.

Under that model, an object falling, under gravity has acceleration -g+ kv (k is the proportionality constant, v the speed. Since that is a function of v, it give the linear differential equation mdv/dt= -mg+ kv. The general solution to that is v(t)= Ce-kt/m-mg/k. For very large t, that exponential (with negative exponent) goes to 0 and the "terminal velocity" is -mg/k.Another common model is to set the resistance force proportional to the square of the speed. That means the net force is -g+ kv2 and v satisfies the differential equation mdv/dt= -g+ kv2. That's a non-linear differential equation but is separable and first order. We can integrate it by writing

dv/(kv2-g)/m= (-1/2√(g))(1/(√(k)v+√(g))dv/m+(1/2√(g))(√(k)v-√(g))dv/m= dt.

Integrating both sides, we get (1/2√(kg))ln((√(k)v-√(g))/(√(k)v+√(g))= mt+ C. For large t, the denominator on the left must go to 0: the terminal velocity is -√(g/k) which, you will notice, is independent of m. This model is typically used for very light objects falling through air or objects falling through water.

Now, we cannot determine the terminal velocity without knowing such things as drag coefficient and such. Could we suspend your subject in a wind tunnel before coming up with an answer?

]]>So it weighs 50 pounds with oh... say 20 pounds of equiptment... knives... some food and other stuff.... a halfling would carry... like spoons...

Plus it is nice to beable to say you know what the terminal velocity of a halfing is... thanks for the help!

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