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More space travel problems: g-forces

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Published: 9 February 2012 (GMT+10)
Spacecraft
Photo: NASA

In a previous article, we showed that interstellar travel had intractable energy problems, simply in achieving the needed high speeds, and the huge impact energies at these speeds.1 And as will be shown, there are other problems, involving what are popularly called “g-forces”.

Actually, the term “g-force” is misleading, because it refers to acceleration due to gravity. Under Newton’s Second Law, F = ma, or force = mass × acceleration. It is used because the weight force is proportional to mass, while acceleration is inversely proportional, so the acceleration of all objects due to gravity is equal. This explains Galileo’s apocryphal experiment of dropping a heavy ball and a light ball from the Leaning Tower of Pisa, and finding that they hit the ground at the same time (except for air resistance).

At the earth’s surface, the acceleration due to gravity is 9.80665 m/s², or 1 g, which will be rounded to 10 m/s² for the “back of the envelope” calculations in this article. Now “acceleration” means change in velocity, which means any change in speed or direction. At 1g, the speed changes by 10 m/s (22 mph) each second, hence 10 m/second-squared.

High g-forces are a big problem for astronauts, fighter pilots and racing drivers. How damaging they are depends on duration and direction. Short duration is obviously better— “Several Indy racing car drivers have withstood impacts in excess of 100 G without serious injuries.”2 But here, the high g-forces are just for a fraction of a second. Even much lower g-forces sustained for even one minute could be fatal.

Direction also matters. The most damaging are “downwards”, when blood rushes into the brain and eyes, where –2 to –3 g is the limit (the negative sign is because of the downwards direction). The least is “forwards” or “eyeballs in”, as in speeding up a car, or an astronaut lying on his back as the rocket shoots upwards. When decelerating, this g-force is experienced in a backward facing seat, which is why they are more protective in crashes. Ordinary people can withstand about 17 g for a few minutes without losing consciousness or suffering long-term damage.3 In general, “horizontal” g-forces, or perpendicular to the spine, are the least dangerous.

In the 1940s and 50s, flight surgeon Capt. John Paul Stapp studied the effects of massive g-forces, using himself as a guinea pig.4 He showed that the human body could survive much more than the 18g previously thought. In one test, he survived a momentary 46.2 g and over 25 g for 1.1 sec. But he was hardly unscathed—in his tests, he suffered from concussions, cracked ribs, and permanent vision damage, although he lived till age 89. His heroic tests led to better design of pilot harnesses, to cope with the higher g-forces that the human body could withstand. Then he showed that pilots were more likely to die in car accidents than plane crashes, so became a leading advocate for car safety belts.

Alien g-forces

With this brief background, how is this now relevant for manned space travel? As with the energy calculations, we will assume merely one third of the speed of light, c/3 or 100,000 km/s (i.e. 62,000 miles per second). Even at such a speed, it would take over 13 years just to reach the nearest star outside our solar system. Yet even this speed would be totally impractical. It is necessary to use some basic physics here, but for those readers not interested, the main conclusions will be in bold.

It seems that 25 g (~250 m/s²) is likely well beyond what the human body can withstand for more than a few seconds. But to be as generous as possible, let’s take that as the limit for sustained acceleration. How long would it take to reach c/3 under such an extreme acceleration? It’s a simple formula for constant acceleration:5

v = at, or t = v/a. That is,

t = (100,000,000 m/s)/250 m/s²

= 400,000 seconds

Since one day is 86,400 seconds, reaching full speed would take over 4½ days!

On an interstellar flight, that is probably not a problem. The problem is if the craft needs to stop suddenly to avoid a crash. Stopping would likewise take over 4½ days, at what is almost certainly a very damaging g-force sustained for so long.

For comparison, going from zero to full speed in 10 seconds, or vice versa, is given by

a = v/t

= (100,000,000 m/s)/10’s
= entails 10 million m/s²
= 1 million g!

[Update: here is a g-Acceleration Calculator—Linear Motion (off-site), where you can input these numbers or any others.]

The stopping distance can also be calculated: since 400,000 seconds is the time it takes to go from 0 to c/3, and vice versa, with a standard formula, we can work out the distance travelled in that time, starting from the initial velocity vᵢ :

d = vᵢ t + ½at²

= (100,000,000 m/s) × 400,000 seconds – ½.250 m/s² × (400,000 s)² (the minus is because it is slowing down)

= 2×10¹³ m

So the stopping distance is 20 billion km (12½ billion miles)!

By comparison, the radius of the earth’s orbit around the sun is only 150 million km (93 million miles), also 1 AU or Astronomical Unit. So we could say that the stopping distance is 133 AU. Even the outermost planet Neptune orbits the sun at only 30 AU, and the famous dwarf planet 134340 Pluto goes no further out than 49 AU (its aphelion = furthest distance from sun). So the stopping distance is over twice the diameter of the outermost planet’s orbit.

Turning

Not only would ultra-fast space ships have problems with g-forces while speeding up and slowing down, they would also have problems while changing direction. Here, the acceleration is at an angle to the direction of motion.

For example, the moon is orbiting the earth—this actually means that it is constantly accelerating towards the earth’s centre of mass, to a first approximation. This is called centripetal acceleration, meaning towards the centre. The force required is centripetal force. This acceleration is nearly at right angles to the direction of motion at all times, producing a nearly circular elliptical orbit. Similarly, the earth is constantly accelerating towards the sun’s centre of mass. So the question arises, how much acceleration would a space craft undergo while turning at the speed we are considering?

There is actually a simple formula for the acceleration of an object moving in a circle of radius r:

a = v²/r.

You would have had experience of this as a driver or passenger in a car. Note that the tighter the circle and greater the speed, the stronger the “lurching” to the side of the car you feel. And on the road, sometimes there are warning signs that recommend a certain speed around a curve for safe driving. The sharper the curve, the lower the recommended speed. If you drive much faster than the recommended speed, the friction of the tyres on the road may fail to provide enough centripetal force. That is, the car starts to skid.

So how does this relate to space craft? Actually, speed is more important because of the velocity-squared term: double the speed, quadruple the g-force. So this is very serious with the huge speeds we are discussing for the space craft. We can use the formula to calculate the minimum turning radius given the maximum allowable acceleration of 25 g:

r = v²/a

= (10⁸ m/s)²/250 m/s²

= 40,000,000,000,000 m

So the minimum turning radius is 40 billion km (25 billion miles) or 267 AU!

In fact, this minimum turning radius is about 5½ times that of Pluto’s aphelion. This means that a super-fast manned space craft would be unable to avoid obstacles with sharper turns than this radius. By comparison, a spacecraft trying to turn as ‘sharply’ as the earth’s orbit would subject its passengers to about 6,700 g.

[Update: here is a g-Acceleration Calculator—Curve, Circuit (off-site), where you can input these numbers or any others.]

Conclusion

Many believe that life evolved on other planets and that it might be millions of years older than humans. Thus they also believe that aliens would have had the time to develop the incredible technologies, as depicted in much Sci-Fi. However, no amount of advanced technology could actually defy or ‘turn off’ the laws of physics that govern our universe. This would be necessary even to travel at a reasonable fraction of the speed of light, let alone faster. Despite lip service to the problems in series like Star Trek, such as “inertial dampers”, these remain firmly as science fiction. The problems in basic physics are insurmountable.

References

  1. Sarfati, J., Alien visitors to Earth? Not with the huge energy shortage and megaton dust bombs, Creation 32(4):40–41, 2010. Return to text.
  2. Human Tolerance and Crash Survivability, ftp://ftp.rta.nato.int/PubFullText/RTO/EN/RTO-EN-HFM-113/EN-HFM-113-06.pdf, 1 January, 2012. Return to text.
  3. Centrifuge Study of Pilot Tolerance to Acceleration and the Effect of Acceleration on Pilot Performance, ntrs.nasa.gov/, 16 January, 2012. Return to text.
  4. Spark, N.T., The Story of John Paul Stapp the “Fastest Man on Earth”, Wings/Airpower Magazine, www.ejectionsite.com/stapp.htm, 16 January, 2012. Return to text.
  5. A special case of aaverage = Δv/Δt, or vf-vi /t Return to text.

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