# Distance to reach terminal velocity

1. Feb 9, 2008

### tomtristan

I am planning an experiment for my coursework in which i am dropping spheres of different mass and calculating their drag. They will be of different sizes, but are made of plastercine so are relatively light. I would guess the heaviest would weigh no more than 20 grams.

Does anybody know roughly how far the heaviest of these balls would have to be dropped before it reaches terminal velocity? Because if possible i want to do my experiment in the classroom without having to drop something out the window and take my equipment outside.

Any estimates would be much appreciated.

2. Feb 9, 2008

### Hootenanny

Staff Emeritus
Welcome to PF tom,

It is possible to calculate the distance taken for your spheres to reach terminal velocity , but I can tell you without calculation, that it's going to take a distance greater than the height of a room.

3. Feb 10, 2008

### tomtristan

Thankyou. I think it might be best if i did an initial experiment from a large height so it has time to reach terminal velocity, and working out the drag coefficient for different spheres. Would the drag coefficients stay constant, so i can use them to work out the drag at velocitys below terminal velocity?

4. Feb 10, 2008

### Littlepig

well, but having in consideration that the esphers are not perfect and alot more factors, i guess that's not necessary...i made that experience and only had to use about 0.5m to get satisfiyng results...^_^

ahh, don't use only 1 esphere of each size...I used 10 equal espheres and the results vary a little, so 1 is a bad aproximation.

5. Feb 10, 2008

### arildno

tom:
In a standard mathematical modelling of a fall, your balls will NEVER reach terminal velocity, but will, in FINITE time, come arbitrarily close to it.

Thus, you have two options:
1. Specify an acceptable error margin on the "terminal" velocity, and we may oblige you with an answer.

2. Develop a mathematical model of fall with air resistance, CONSISTENT WITH OBSERVATIONS, that DOES predict a finite time for terminal velocity to be reached.

I'm not saying that 2. is impossible, but I will strongly advise you to choose option 1. instead.

6. Feb 10, 2008

### tomtristan

If instead i was to ask what the error margin would be if i was going to drop the spheres from 2 metres, would be be able to oblige me with an answer?
My experiment is not going to be hugely accurate anyway, as the density of the spheres won't be even, as they have to contain a magnet, because i am dropping the spheres through a magnetic circuit and using the induced emf to calculate velocity.

7. Feb 10, 2008

### arildno

Sure, then your ACTUAL question woulkd be:
How close will I be to the terminal velocity during a fall of length two meters?