Nuts and Volts - September 2008

IT’S A DRAG

Drag is a force that opposes the motion of an object. If it’s stationary, then the force of drag equals zero, and the faster it moves, the greater the force of drag. In the case of a falling object, the force of gravity governs the speed at which it falls until it reaches a terminal velocity balanced by drag. The two forces — gravity pulling down and drag pulling up — equal each other at terminal velocity.

The force of drag acting on a body moving through a medium can be described with this formula:

F_d= ½ ρv²C_dA

where

• ρ is the density of the medium the body is moving through

• v is the velocity (speed) of the body

• C_dis the body’s coefficient of drag

• A is the frontal area of the body

These factors are easy to understand except for one: C_d. The coefficient of drag is a dimensionless constant. Being dimensionless means it has no units like meters, seconds, or grams. The C_dfor a flat plate is around 1, while more

streamline bodies have a C_dless than 1.0.

The weight of a parachute and its payload doesn’t change in any real way for a descent from near space. Since the drag force (F_d) must equal the parachute and payload weight, as the air density (ρ) increases, the velocity squared must decrease in proportion (assuming C_dand A for the parachute don’t change appreciably during the descent). This indicates the square root of the parachute’s descent speed is inversely proportional to the air density.

Source: http://en.wikipedia.org/wiki/ Drag_coefficient

the tapes wrap around the end of the canopy and into the inside of the parachute. Now you can sew the seams between gores and their reinforcing tapes together. There should be a small loop at the bottom of the parachute where the twill tape was wrapped around.

Now sew the twill tape onto the canopy. As it’s sewn, the sewing machine is also sewing the gores together. The ends of the twill tapes must be sewn extra strong. Wrap the end of the twill tape around the underside of the canopy and run extra stitches

through it and the canopy as illustrated in Figure 13. That’s it for making a parachute canopy. The next column will discuss the shroud lines and the parachutes spreader ring. There will also be a recovery aid to attach to the parachute.

A PARACHUTE DESCENT FROM NEAR SPACE

■ FIGURE 13. The light gray bars represent closely spaced stitches that reinforce the twill’s attachment to the parachute canopy.

■ FIGURE 12. Images — recorded every 1/3rd of a second — showing the opening of a deployed parachute. The fully deployed parachute appears at the top of the frame and looks like a semicircle with a zig-zag edge.

Let’s look at two aspects of parachute performance in the near space environment. First, a parachute returning from near space experiences an extreme change in air density and pressure. A parachute deployment at 100,000 feet takes place at an atmospheric pressure of 10 mb, or 1% of the average air pressure at sea level (1,013 mb). As the parachute descends, the air density becomes greater and the parachute becomes more effective at slowing

the payload down. The parachute’s drag — and therefore its ability to slow a payload down — depends on the air’s density. So, let’s compare a parachute’s descent speed as a function of atmospheric pressure to see if it agrees with the equation for drag.

A parachute descends at a speed where the drag it creates is equal to the weight of the parachute and its payload. When the two oppositely directed forces are equal, there is no net force acting on the parachute and therefore, it experiences no acceleration. A constant velocity is the result of no acceleration. Now according to the equation for drag, the force a parachute experiences is proportional to its speed and to the square root of the air density. Using data from a previous near space mission, I created a chart comparing the square root of the air pressure (a good surrogate for air density) and the near spacecraft’s descent speed as a function of altitude.