Physics and Star Trek/The impulse drive and inertial dampers

The Impulse drive is the sub-light speed engine that the Enterprise uses when it is not travelling at warp speed. It's an excellent piece of technology, it allows the crew to travel between planets fairly quickly, and Starfleet Academy cadets practice flying out to Saturn and back using it.

As excellent as this technology is, it would run into a few practical challenges in being implemented. Generally there are three major problems, acceleration, time dilation and energy. These are discussed separately.

Acceleration under impulse speed.
Imagine the scene - Captain Picard wants to examine a nearby planet a bit more closely, and he gives the order to Lt. Commander Data to head that way at "half impulse". According to the show, "full impulse" is light speed (300 million kilometres per second) so half impulse would be 150 million km/s. Let's assume the Enterprise was at a standstill to begin with, and that it took fifteen seconds to reach half-impulse speed.

The acceleration in this case would be 10000 kilometers per second, or (converting it to metres), 10 million metres pers second. Unfortunately, we run into a small problem here. An acceleration of this magnitude would be so severe as to dissolve the molecules in Captain Picard's body into their component atoms - there wouldn't even be any blood, as the blood itself would decompose.

To understand this, consider the acceleration due to gravity, which is (very) approximately 10 metres per second (it is actually closer to 9.8 m/s). This is called 1 "G". We experience this acceleration all the time, obviously, in a downward direction as the earth pulls us towards its centre. Acceleration in any direction can be experienced. Consider a typical family car which can go from 0 to a speed of 100 km/h (60 mp/h) in around 8 seconds. 100 kms per hour is (roughly) 28 metres per second. So, to get to this speed in 8 seconds requires an average acceleration of 3.5 metres per second. A very expensive sports car might achieve this in four seconds, so now we have an acceleration of around 7 m/s, over 4 seconds.

So a high performance sports car can only barely compare with the acceleration due to gravity. Fighter jets can do much better however. Consider a jet ambling along at 500 mph (220 m/s). It then fully opens the throttle and accelerates to "Mach 2" ("Mach 1" is the speed of sound, 740 mph or 330 m/s, hence Mach 2 is around 1500 mph, or 660 m/s). Fighter jets can do this in about 8 seconds. Consider the mathematics again, we start at 220 m/s and accelerate to 660 m/s over a period of 5 seconds, this is 440/8 or acceleration of 55 metres every second.

However jets most definitely do not accelerate at this rate. The jets can do it, but the pilots can't; they tend to fall unconscious very quickly. An acceleration of 55 m/s is roughly equal to 5.5 "G" and our human bodies were simply not designed to cope with this. The blood in our bodies drains to the opposite direction of the acceleration, and away from the brain, hence the unconsciousness. Fighter pilots wear special outfits which compress the body, in an attempt to prevent the blood pooling in the legs during acceleration. Research has shown that the human body cannot handle accelerations above 3G for any sustained period, and cannot handle accelerations above 7G for anything more than a second or two.

At what rate does acceleration become fatal? Consider a car crash - a passenger is travelling at 60 mph (28 m/s) and hits a brick wall head on. Generally this would kill the passenger. If the passenger went from 60 mph to zero in a time of 50 milliseconds (a typical duration) then the acceleration would be 28/0.05 or 560 m/s. Generally, any acceleration above 500 m/s (or 50 "G") will have fatal consequences. (Most safety devices in cars such as "crumple zones" and "air-bags" operate by trying to increase the time for the change in acceleration to be felt, thus lessening the actual rate of acceleration, and hence reducing injury).

So getting back to Captain Picard, in getting up to "half-impulse" over 15 seconds, he would experience an acceleration of 10 million metres per second, which is roughly 1 million "G". The human body can't function above 5G, and 50G is fatal. It can safely be said that 1 million G would pulverise the atoms of his body into near-nothingness.

Unfortunately, if we reduced the acceleration to the upper human limit of 3G (an acceleration of 30 m/s per second), getting the Enterprise to "half-impulse" speed would take nearly 58 days, or just shy of two months. This doesn't make for good television.

The inertial dampeners...