Drag

So we finished our first flights, and the rockets didn't go quite as high as we had anticipated. In fact, not even close. What's up with that? Our calculations for altitude took into account everything except air resistance, or drag. According to G. Harry Stine's Handbook of Model Rocketry (Sixth Edition) (published 1994 by John Wiley and Sons), "Aerodynamic drag lowers the computed drag-free maximum altitude of a model rocket by about 50% (for low- powered models) to as much as 80% (for high-powered models). It's easy to see that we shouldn't be surprised by the fact that a rocket only flew 119 meters when we predicted it would go up 295 meters.

But what is drag? Simply put, drag is the cumulative effect of several aspects of motion through fluids acting upon the rocket. When we study fluid flow in Physics, we talk about laminar flow, turbulent flow, Bernoulli's equations, and other aspects of fluids (and air is a fluid!) that affect the way objects move in a fluid stream (or the way fluids move when confined in something like a pipe.) To think of the impact that fluid flow can have on an object, try a simple experiment next time you are driving down the highway: stick your hand out of the car window (I know your mother told you never to do this) and feel the effect of the air flow on your hand. Vary the aspect of your hand into the flow and see how it affects the movement of your hand. Your rocket undergoes the same kind of forces. Drag is a force - think of it as fluid friction and it will always oppose the motion of the rocket. We can minimize drag in our designs, but first we need to understand the mechanisms that cause drag.

Drag is actually the accumulation of several issues that we can talk about, and so we'll discuss four different types of drag. There are others and you can feel free to research them further! The first is pressure drag. Pressure drag is caused by the difference in pressures between the front of the rocket and the back of the rocket. As a rocket moves through the air, it hits the air molecules in front and this builds up pressure in front of the rocket. The less stream lined the rocket (a stubby nose cone), the more pressure is built up in the front. At the same time, an area of low pressure exists behind the rocket due to a higher velocity flow of air around the end of the rocket. This difference pressures between the front and rear of the rocket create a retarding force
that slows the rocket. The faster the rocket, the greater the retarding force.

A second form of drag is friction drag and it is what the name implies - the drag caused by molecules of air rubbing against the surface of the rocket while it is in flight. This is the same kind of friction we get when we rub our hands together, and in fact, at high enough speeds, can generate significant heat. Fortunately, we don't reach those speeds. Friction drag can be minimized by maintaining super smooth surfaces on our rockets.

A third type of drag is obstruction drag. This is drag due to having things sticking off the side of the rocket and interfering with the overall flow of air around the rocket. Things like launch lugs and irregularities in the surface joints on the rocket contribute to this type of drag.

Finally, we'll look at induced or lift drag. This is drag caused by Bernoulli effects around the fins and corners on the rockets. Due to an increase of the velocity of air on one side of the obstruction, a low pressure area is created and we get a lift effect similar to the wing of an airplane. At the tips of the fins or the rocket, there is turbulence where the high and low pressure regions that caused the lift meet and this creates additional drag on the rocket. Airplanes have a similar issue at the tips of the wings - you may have noticed that some wings have a fin-like attachment that is perpendicular to the wing mounted on the wing tip to minimize the effect of induced drag.

So how do we quantify drag? Drag can be found using the equation:

Where D is the drag force (in Newtons), r is the density of the fluid (we can use air at 1.29 kg/m3), V is the velocity of the rocket, Cd is the drag coefficient (found experimentally, generally with a wind tunnel, and A is the front head-on area of the rocket. So what can we change to help us out?

There isn't a whole lot we can do about air density. Air density decreases with temperature and with altitude, so we'll have less resistance on warmer days. We can lower the value of area by building thinner rockets with sharper, smaller fins and less obstructions. Speed is important - drag increases as a factor of the square of the speed (twice the speed yields four times the drag). Use smaller engines! Finally, shape and design of the rocket can influence the coefficient of drag.

We can approximate our drag by finding the difference between our expected maximum altitude and the actual
altitude and call the difference due to drag. If we build a wind tunnel, we can make actual measurements of drag that will yield a more satisfactory estimate of the effect.