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Real-World Versus Model Parachutes

The issues designers of real-life parachutes worry about are sometimes the same and sometimes different from the ones your students face.

Steering is something the students might like to do with their chutes, but have no means to do. Jumpers can deliberately spill air out of one side of the parachute by means of cords attached to the skirt of the chute. This makes the parachute fall faster, but it allows the jumper to guide the direction of travel, rather than simply going in the same direction that any wind blows.

Deploying a packed 25 kg bundle of cloth and cords into a fully inflated parachute is critical in real life but not with your students -- many open up their chutes before dropping them. Some real parachute systems use a smaller pilot chute to pull out the main canopy.

Speed and load are key differences between the performance of model and real parachutes. People in free-fall drop from around 54-80 meters/sec (120-180 mph) -- their speed after chute deployment slows down to 3.7-6.7 meters/sec. The model parachutes your students will build fall at a rate of 0.8-2 meters/sec or faster. Scaled to the size of the chute, this means the models are proportionally falling faster -- for a half-meter-wide model, this comes to 1.6-4.0 diameters per second, whereas for a 7-meter-wide real chute, the real-chute descent speeds above are more like 0.5-1.0 diameters per second.

This is not surprising, considering that air drag per unit area is a function of the square of the speed -- more than 10 times as great at 6.7m/sec as at 2 m/sec. If you were to make a model by scaling down both a chute and its human passenger by the same factor with respect to their linear dimensions (height, width, etc), for example by a factor of 10 -- so that the chute area decreased by a factor of 100 and the passenger weight by a factor of 1000, and the loading per unit area of chute decreased by a factor of 10 -- the descent rate would not decrease by a factor of 10 but only by the square root of that, or 3.17; so that in diameters per second the model would descend 3.2 times as fast as the real chute.

Moreover, the specifications for real parachutes would never ask you to make something that descends as slowly as the models, because the square-of-the-speed relation comes into play here too -- to give a terminal speed twice as slow, a canopy would have to have four times as much area, which means that when it first opened at the human’s free-fall speed, it would exert four times as much force on the passenger -- a human user would be injured or killed by slowing down too abruptly, and in trying to bear the forces needed to slow down the parachute system quickly the parachute itself could rip and tear, which would lead to disaster for the user.

Another difference that size makes involves multi-layered parachutes. For a model parachute, the turbulence of the bottom canopy would not interfere as much with a second layer. For full-scale chutes this turbulence extends a much longer distance downwind from the bottom chute. This would make it impossible for a nearby canopy layer to stay inflated as it descends.

Load has implications for stability, at both scales. Students who make parachutes indoors and then test them outside can sometimes find that a turbulent gust of wind can cause the canopy to collapse. One reason for a designer choosing to use more weight rather than less is to maintain enough pressure in the canopy to have it keep its shape when a gust hits it. This was a major problem with the designs of the chutes that were dropped from the top of the football stands during a windy day.

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