More space travel problems: g-forces
Published: 9 February 2012 (GMT+10)
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.
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.
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.]
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.
- 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.
- 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.
- Centrifuge Study of Pilot Tolerance to Acceleration and the Effect of Acceleration on Pilot Performance, ntrs.nasa.gov/, 16 January, 2012. Return to text.
- 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.
- A special case of aaverage = Δv/Δt, or vf-vi /t Return to text.
Dear Mr [sic] Sarfati
This is an interesting article in that (a) I don’t think many people—religious or otherwise—would dispute it and (b) why you see the need to make the points. They neither prove nor disprove the creation story or do the same for evolution.
Of course, if by ‘life’ you mean Captain Kirk type life then yes, it’s pretty certain that we will never be able to undertake such travel. However, micro-biological life may be able to do so and ‘seed’ other planets. Certainly it is known that basic building blocks of life such as amino acids can survive in deep space.
None of this is proven of course but it is the most likely way in which ‘life’ could travel.
At the speeds we are talking about, the g-forces would probably be too much for any multicellular life. But even the panspermia you are talking about has problems of its own. A major one is that any meteorite or comet carrying these spores would be burned by the heat from atmospheric friction (see Panspermia theory burned to a crisp: bacteria couldn’t survive on meteorite). Also, amino acids are far removed from life; see for example Origin of life: the polymerization problem.
(Dr) Jonathan Sarfati
Very good article on the insurmountable scientific problems with travelling at lightspeeds. Sci-Fi is fiction and is meant to be enjoyed as fiction. However there are developments that have developed from these shows like “tablets” which have become reality—I’m using an ANDROID tablet right now. Sometimes imagination can drive something into reality. Inertial dampers at this stage are still imagination but someday may become a reality. God created man as the pinnacle of His Creation and gave man the ability (not without GOD’s input) to invent devices that can use the laws of this universe to do many things-even though it is a fallen world. I do believe that it may be possible someday for man to travel to distant planets-only with God’s blessing and assistance if it is HIS will.
Thank you for your comments.
All the same, an android is not the same level of problem as inertial dampers. An android is based on no new physical law, but applications of semiconductor physics; the previous limitations were merely practical not theoretical. Inertial dampers would need to defy known physical laws. So the difference is one of kind not degree.
As a Christian, I have never liked the reasoning of the various people who are into the naturalistic philosophy of science, trying to tie the bible to any point of time’s science, or measure the bible only by what man’s science currently knows now.
As is widely quoted, if the bible had been tied/re-written to 19th century science, we would now have an out of date bible.
[Jonathan Sarfati responds, JS]: We agree. See for example Galileo Quadricentennial: Myth vs fact.
In the same way I believe it can be unwise to argue for a Christian position, from where science is today. There is so much that science does not yet understand about the fabric of space, matter energy, and many other things, and it would be sad to see a good Christian position discredited because it was tied too closely to where science is today, as suddenly science learnt something more about what God has created and how it all works.
[JS]: Our position against alien life is fully based on foundational biblical teachings. Compare the above Galileo article with Did God create life on other planets? Articles like the g-forces one are applying science ministerially not magisterially. See Biblical history and the role of science for further explanation of this distinction.
I recall hearing about my forebears laughing over the ‘good’ science that had proved that all the air would be sucked out of people’s lungs if they went above, I think was it, 50 mile per hour(?), yet trains and early cars soon did, and the occupants were still around to talk about it afterwards.
[JS]: OK, we sometimes receive such hearsay, but when people are asked to provide a source from a reputable scientist of the day, the trail mysteriously goes cold. The whole story sounds most suspicious, since people were known to survive gales of over 50 mph which would have the same effect as travelling at 50 mph through still air. And they probably knew about cheetahs that can exceed 50 mph in short bursts. Similarly, although there are apocryphal claims that scientists proved that heavier-than-air flight was impossible, it’s most unlikely that any scientist who had seen a bird or bee could be so dogmatic.
And what scientific law in particular did these people in your example appeal to? The only one I can think of that would be mostly applicable would be Bernoulli’s principle of pressure drop with increasing fluid (gas or liquid) speed. Then I would like to see the equations worked out. In my case, I explained the physical laws and provided the equations.
With any future advances in the knowledge of Creation and the nature of time, space, matter and energy, the same might well happen with space, or the means of interstellar, travel.
[JS]: As I hope I have explained, the counter-example you adduced seems to be grounded in neither historical fact nor even the science of the day. Mine is grounded on Newtonian physics, and relativistic physics, with mass increased by the Lorentz factor, would make the problem even worse.
So the arguments against evolved aliens coming across space form other stars, should perhaps better rest simply on the biblical account of no such alien evolution having happened, and there being no evolved intelligent aliens to travel to us, because of God’s completely reliable description of His Own works of creation.
[JS]: CMI’s approach is both-and not either-or.
Hope this helps.
PS: Another issue that has been raised, against the issue of deadly collisions, is that they were elastic, meaning no loss of kinetic energy. But macroscopic objects could not collide elastically at such speeds. The reason is that shock wave of the impact on the front end of the object can travel no faster than the speed of sound in that object. At the speeds we are talking about, this would be far too slow: the back end would still be travelling forward before the ‘information’ of the impact reaches it. So the object would be crushed by the collision before the elastic forces could come into play.
That might put a “little” problem on interstellar flight. Although I am curious on the feasibility of warp drives to physically warp or move space with the space craft, so technically, the space craft itself isn’t going nearly that fast (almost 0 relative to the speed of the warp field), but the little “bubble” that it is being transported in is traveling up to hundreds if not thousands of times faster than that. Would such a device (if possible) solve the problems or just make them worse?
Thank you for your comments. Of course any Star Trek fan knows about warp drives. But they are still definitely fiction. My arguments in this article and Did life come to Earth from outer space? show that a problem arises even with very high sub-light speeds (like Star Trek’s ”impulse engines”).
One problem that springs to mind with warping space is that space carries all sorts of debris. As shown in the linked article, even a tiny grain at such high speeds would cause enormous damage because of the high kinetic energies involved. A compression of space, such as a proposed warp drive, would cram all those particles into a smaller volume, increasing the particle density. Thus it would magnify this problem.
Since writing those articles, I found a secular astronomy page that recognizes the problem with space debris (although this uses c/2 instead of c/3):
At 50 percent the speed of light which is the minimum for interstellar travel you will cover enough distance in a short amount of time, that your liklihood of encountering a large interstellar dust grain becomes significant. Only one such impact would be enough to cause severe spacecraft damage given the kinetic energy involved.
A large dust grain might have a mass of a few milligrams. Traveling at 50% the speed of light, its kinetic energy is given non-relativistically by 1/2 mv^2 so E = .5 (0.001 grams) x (0.5 x 3 x 10^10 cm/sec) = 1.1 x 10^17 ergs. This, equals the kinetic energy of a 10 gram bullet traveling at a speed of 1500 kilometers per second, or the energy of a 100 pound person traveling at 13 miles per second! The point is that at these speeds, even a dust grain would explode like a pinpoint bomb, forming an intense fireball that would melt through the skin like a hot poker melts a block of cheese.
The dust grains at interstellar speeds become lethal interstellar ‘BB shots’ pummeling your spacecraft like rain. They puncture your ship, exploding in a brief fireball at the instant of contact.
Your likelihood of encountering a deadly dust grain is simply dependent on the volume of space your spacecraft sweeps out. The speed at which you do this only determines how often you will encounter the dust grain in your journey. At 10,000 times the space shuttle’s speed, the collision vaporizes the particles and a fair depth of the spacecraft bulkhead along the path of travel.
But the situation could well be worse than this if the interstellar medium contains lots of ice globules from ancient comets and other things we cannot begin to detect in interstellar space. These impacts even at 0.1c would be fatal …we just don’t know what the ‘size spectrum’ of matter is between interstellar ‘micron-sized’ dust grains, and small stars, in interstellar space.
My gut feeling is that interstellar space is rather filthy, and this would make interstellar, relativistic travel, not only technically difficult but impossible to boot! Safe speeds for current technology would be only slightly higher that space shuttle speeds especially if interstellar space contains chunks of comet ice.
Hope this helps.