How to Calculate the String Angle of a Kite vs. a Balloon

What? This looks just like the forces for the balloon? OK, it does look similar—but there is a big difference. For the balloon, there is that upward-pushing buoyancy force, and it’s just one value. It doesn’t change when the wind speed increases. For the kite, the upward pushing force is the lift, and it DOES depend on the wind speed. So it’s not the same. Just consider the case when there is zero wind. The drag force will be zero, which means the lift is zero. The kite won’t fly—it just falls down and it’s sad.

Again, I get two force equations that I can use to eliminate the unknown value of T. With that, I get the following expression for the angle of the kite (θ_k). Actually, I put a subscript k on a bunch of stuff so you could see it’s different than the values for the balloon. Oh, air still has the same density for both objects.

OK, I’m about to make a plot of the flying angle for both the balloon and a kite at different wind speeds. But before I do that, let’s think about the minimum speed to fly this kite. In order to lift off the ground, the lift force must be at least equal to the weight of the kite. I can then solve this for the wind speed. Anything lower than this and you won’t have a flying kite.