Homework Help: Velocity final estimate on frictionless craft

1. Feb 4, 2010

vitologarcia

1. The problem statement, all variables and given/known data
I am trying to calculate the estimated final velocity of a R/C hovercraft i am trying to built. The craft's weight is 6lbs and it is powered by a electric ducted fan that produces 21.3 ounces of thrust. Assuming this craft is actually hovering (no friction with the ground) and has an estimated drag coefficient of .8 (surface area of the front is .33m^2). Time is 6 minutes if needed (half of my battery).

2. Relevant equations
F=ma
a=f/m
a=(Vf-Vo)/t

3. The attempt at a solution
F=1bf=4.448N
w=f=mg ----- 6lb=m(9.8) ( i am confused with my units)
m=.816
a=F/M=4.448N/.816=5.39m/s^2 ???

I dont know where to go from here, I am just trying to estimate how fast (constant final velocity) i can get this to go on half my battery so that I know how far it will go before I need it to come back.

2. Feb 4, 2010

Staff: Mentor

Welcome to the PF. I'm not of any direct help, but the wikipedia page has the general equation for air resistance and other helpful info:

http://en.wikipedia.org/wiki/Air_resistance

It would seem that you would just equate the available driving force of your horiqontal duct with the wind rresistance to find out your max speed, but again, I'm no ME.

3. Feb 4, 2010

vitologarcia

Thanks
is there anyway you can help me with the acceleration? and my mass? getting it in the right units?

4. Feb 4, 2010

Staff: Mentor

The sum of all forces F = ma. Convert everything to mks units (meters, kilograms, seconds), and you should be fine. You can calculate your initial acceleration, which will be when there is no wind resistance, and that acceleration will gradually go to zero as you get to speed where the driving and retarding forces match.

If you're familiar with calculus, you can calculate the velocity as a function of time during the ramp up to speed. If not, then you can estimate it in a piecewise fashion (or even use an Excel spreadsheet to get a pretty accurate estimate).

5. Feb 4, 2010

vitologarcia

actually i am 15 so i dont know calculus but yeah...
8lb=2.72kg

but one is weight and the other is mass, does that matter?

6. Feb 4, 2010

Staff: Mentor

I'm pretty fuzzy on the Imperial unit system, but I believe when you use the conversion 1 = 2.2lb/kg, it's actually pound_mass, as opposed to a pound_force. But don't quote me on that.

Where did you get 8lb = 2.72kg, BTW?

7. Feb 4, 2010

vitologarcia

sorry that meant to say 6lb=2.72kg
and thanks for all lets see what comes out of this hehe