Calculating Drag on a Weather Balloon at 4m/s

[retang]

Hi,

I am trying to caculate the aerodynamic drag on a weather balloon that's climbing through the atmosphere.

Of course, the velocity is very low here, about 4m/s.

Such a balloon is an almost perfect sphere.
So I am trying to fill in the drag equation, but I still have two unknown variables.
As one can see on:
http://www.grc.nasa.gov/WWW/K-12/airplane/dragsphere.html
Apparently no one sphere is the same, and there are different values for diferent speeds. The wikipedia page on drag simply states the the Cd numer is 0.47, but on the NASA page you can read that it's between certain values (0.07 and 0.5) (and then I still need to know the reference area

So I need to know how I can calculate the reference area, and the drag coefficient.
http://www.grc.nasa.gov/WWW/K-12/airplane/dragco.html

The velocity of such a balloon going up is about 4m/s, so it's on the low side, probably.

I need these values, so that I can caculate how much gas there was contained in a balloon with a given mass and a given payload mass, and a given airspeed.

 

[russ_watters]

If the balloon is at constant speed then the drag force equals the buoyant force.

 

[retang]

The problem is, is that the buoyant force is not known. Only the speed of the balloon is known, and the weight of the parts is known.

 

[russ_watters]

The problem is, is that the buoyant force is not known. Only the speed of the balloon is known, and the weight of the parts is known.

OK, I see what you mean (sorta).

The area is just the cross sectional area.

For Cd, I guess I would just estimate the Reynolds' number and then pull cd from the graph. If Rex is greater than 10^4, I'd probably use the smooth object line. This will be a very inexact way to find the size of a balloon though.

 

[Paul.Nord]

Any luck parameterizing this?

I'm working on the same problem myself. We do know the lift. The balloon is filled until it will lift 2.5 kg. We then attach a 1.3 kg payload. It appears that it quickly reaches a terminal velocity of about 4 or 5 m/s. That's easy to achieve with a simple drag coefficient which scales with the square of velocity.

deltaV = 0.5 * g * (Lift-Mass)/(Lift+Mass) - Drag * v * v

I'm modeling the lift as a simple Attwood's Machine. The Lift is equivalent to the the mass of the air which is forced downward when the balloon moves up. And it must move down at the same rate at which the balloon moves up. Of course, the momentum of this air is lost and won't help to keep the balloon moving if something tries to slow it. So, perhaps this differential equation makes no sense without the drag term.

Is it safe to ignore how the Reynolds' number might change with altitude, velocity, and balloon diameter? I'm told that these balloons tend to maintain the same assent rate throughout their flight. In this case, the equation above can produce a realistic parameterization of the flight path.

Is there a better way?

 

[Chestermiller]

Step 1 : estimate the Reynolds number from the balloon speed, diameter, air density, and viscosity. Do this for a few altitudes to see how much it varies (at typical combinations of atmospheric temperatures and pressure). The temperatures and pressures in the atmosphere on average can be obtained on line or from the US Standard Atmosphere.

Step 2: See if the range of Reynolds numbers matters with regard to whether the balloon is rough or smooth. If it does, assume that the balloon is rough.

Step 3: Estimate the drag force. The reference area is the projected area of the sphere.