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Use the equation constant acceleration:

 Hookes Law

If you drop from the top of the slide then the initial vertical velocity will be zero. So:

 Hookes Law

Why would a practical drop slide have to be taller than the value you calculated?

After falling for one second you would be traveling at 9.8 m s-1 and your landing would not be soft. As a result there needs to be a long curved section where your vertical velocity is gradually changed into horizontal motion. Drop slides are usually defined by the distance from the top to the bottom, not the vertical drop distance. Even so a 12 m total drop can still seem quite daunting when you are sitting on the edge.

Another way of achieving personal microgravity might seem to be to use a freefall parachute jump from a plane or a balloon. A typical freefall jump is made from around 3800 m and the parachute is opened at an altitude of 750 m. The skydiver might experience around 60 s of ‘freefall’. If g is taken as 9.8 m s-1 comment on whether this is truly free fall.

If the sky diver were truly experiencing freefall then they would accelerate downwards at a rate of 9.8 m s-2. Assuming that their initial vertical velocity was zero then in the sixty seconds they would fall a total distance of:

 Hookes Law

Or 18 km to two significant figures. Clearly they are not in true freefall, if they were they would fall the 3 km to the deployment altitude in only 24.7 seconds. A skydiver, like all other objects falling through a fluid, has a terminal velocity. As their speed increases, so does the drag force that is acting to slow them down. The actual terminal velocity will depend on the shape the sky diver adopts and their weight but the 185 km/h figure quoted is a rough guide for most parachutists.

The sky diver will be traveling at around 185 km/h when they open their parachute. From a simple estimate calculate the maximum period of microgravity for the sky diver.

 Hookes Law

The simplest assumption that we can make is that the skydiver accelerates at g until they reach the terminal velocity. At this point their speed becomes a constant. This also gives the maximum possible estimate of freefall time as the time to reach terminal velocity can only be increased by adding a drag force to limit the skydiver’s speed. This would immediately cancel the conditions for true freefall. 185 km/h is equal to 51.4 m s-1. So:

 Hookes Law

What is the figure more likely to be?

In fact the drag force starts to build up the moment the skydiver starts to fall. The result is a gradual approach to terminal velocity as shown in the dashed line in the sketched graph and so the time spent in true microgravity is essentially zero. Sky diving might be thrilling in itself but falling through air is not a useful way of generating the microgravity needed by scientific researchers.

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