Built on Facts

Sail Away

Weekend posting here is usually pretty light, but it’s only the second day here so I think a little extra is a nice way to kick things off. How about a little bit of solar sailing, since it fits pretty well with what I’m teaching in my intro class?

We all know light carries energy. Go outside on a sunny day and you can feel the energy being absorbed by your skin. You feel it as heat, but visible light energy allows you to see and ultraviolet light will induce chemical changes which will finally result in your body making itself a bit more tan. What’s less apparent is that light also carries momentum. Take two electrons, separate them by some large distance, and wiggle around the first electron. The wiggling electron is an accelerating charge, and so it induces electromagnetic waves which propagate outward and eventually hit the second electron which makes it wiggle as well.

That electron wasn’t moving before the wave got there, and it is moving after. So it didn’t have momentum before, but it does after. Therefore the incoming electromagnetic wave has to carry momentum.

It’s a pretty snazzy revelation, one which took some of my students by suprise. “Isn’t momentum given by mass times velocity, and doesn’t light not have a mass?” Yes and yes, but it turns out that the old p = mv formula only works for things with mass. We skipped the technical details since it’s just an intro class, and fortunately the resulting formula for the momentum of light is very easy to work with.

Find the power per area of a beam of light. (For sunlight at the surface of the earth, it’s about 1000 watts per square meter.) Call that quantity S. The time rate of change in the momentum p of something with that light shining on it is

i-d4bb9fe09d6b78eb832985821d8a307f-1.png

Where A is the area which the light is shining on. You can more conveniently write this as a pressure (call it P)

i-88516ca505d84f969b7ab15a965c3fb3-2.png

Not bad. So why is it that we don’t feel the pressure from the sun when we stand outside? It’s because the speed of light c is such a huge number. If you plug in the numbers, you’ll find that the radiation pressure from the sun is something like 4.8 x 10-10 pounds per square inch. Way, way too tiny to measure.

But if you have a big sail in the vacuum of space where there’s no friction…

Let’s see, a square mile of reflective sail would have about 4 pounds of force. That’s not very much, but it requires no fuel at all and will keep going as long as the sun shines. To an aerospace engineer that sounds like something of beauty.

Comments

  1. #1 Mike Wilhelm
    August 2, 2008

    First post ;)
    First blog read from this rss..

    I think I’m going to like this Blog

  2. #2 Gordon Pasha
    August 2, 2008

    Hello

    When read with google reader, your new blog appears as (title unknown) where the title of the blog is supposed to appear.

    Regards
    Gordon

  3. #3 Vernon Balbert
    August 2, 2008

    It’s been 30 years since I took high school physics, but considering the topic of this and that NASA is planning on sending a solar sail test probe out, I thought I’d like to know how much pressure it will have. According to Scientific America, this probe will have a solar sail about 100 square feet (9.3 square meters.)

    http://www.sciam.com/article.cfm?id=space-sail-voyage

    As I said, it’s been a long time since I did this kind of stuff. (I fix computers, not mathematical calculations for physics.) I can do the math, but what is the unit of measure? The calculator gives me ~0.0058 but ~0.0058 of what? (FWIW, I used square feet and miles per second for area and c.)

  4. #4 epsilon
    August 2, 2008

    I came across this blog on Pharyngula. I’m currently an undergraduate student in math, and I love physics. After reading through some of the old posts, I have to say that this is now one of my favorite blogs. Keep up the good work.

  5. #5 Uncle Al
    August 2, 2008

    One pound of thrust is 2.0833×10^9 in^2 or 1.344×10^6 m^2 of solar sail best case. 5 micron thick polyimide film CP-1 has an areal density of 5 g/m^2 – 6.7 metric tonnes for the naked sail (10 tonnes for Kapton), plus aluminization and physical plant. Nominal 1 lb thrust/22,000 lbs vehicle best case. Convert to gees. Price CP-1 (!!!) or Kapton.

    The sail blackbody emits. The visible mirror must be a poor IR emitter on the other side, maximizing net thrust. If it cannot cool by IR emission it heats. Equilibrium temp vs. failure temp of micron membrane compositions. Aluminum sublimation and sputtering (solar wind) in hard vacuum.

    What steering line can be kilometers long and respond to a pull, proximal vs. distal? A pull against what to what? Thrusters? Membrane ripples and other deformations, then…

    Distribution of force/area for light pressure on a taut (but stretchable – square kilometers) mirror membrane bulges into a concave mirror on the lighted side. Don’t have your capsule or lines at the focus or cutting a caustic. Poof!

    Solar storms and mass ejections. Magnetic fields and inductance (no dielectric mirrors for the added mass). Anything containing magnetohydrodynamics is in a world of hurt – bow shock from going supersonic vs. the solar wind.

    The solar constant at Earth orbit is 1368 W/m^2. 1.344×10^6 m^2 solar sail as an off-axis paraboloid is a 1.8 gigawatt-continuous space weapon for melting cities. Scale that for losses any way you like.

  6. #6 erik542
    August 2, 2008

    Well dp/dt = d(mv)/dt = d^2(mx)/dt^2 = m*d^2(x)/dt^2. A = x^2.So we have m*x/(t^2*x^2) on the left. That simplifies down to m/(t^2*x). Solve for S. x/t * m/(t^2*x) = m/t^3. Our units are kilograms / second^3 = m*x^2/(t^3*x^2) = Watts / Length^2 hence Power per Area.

  7. #7 Kobra
    August 2, 2008

    4 pounds of force for a square mile? That would hardly move. :P

  8. #8 Alex
    August 2, 2008

    Found this blog through Pharyngula. Cool stuff, I will definitely read again.

  9. #9 Matt
    August 2, 2008

    Vernon: You can use any consistent set of units, but I’d recommend SI, and then converting the final SI answer to something else at the end if you want. So if S in in watts/meter^2, c has to be in meters per second, and the pressure will be in newtons/meter^2.

    Google can actually do all this for you. “(1000 watts per meter^2)/(speed of light) in pounds per square inch” as a search string will actually do the calculation and unit conversions for you.

  10. #10 joergen geerds
    August 2, 2008

    Drop the imperial units, they shouldn’t be used anywhere in science. Physics is using SI, and so should you.

  11. #11 bigjoh756
    August 2, 2008

    Only the primitive nations of the world use imperial units in this day and age.

  12. #12 Odysseus
    August 2, 2008

    Nice topic for a start. The momentum thing p=mv actually still works for photons once you consider the relativistic mass instead of the rest mass. High school physics should get to you to p=hf/c. I remember an interesting post on the xkcd blag a while ago which considered ways to make solar sails a little more effective.
    Indeed just a few N of accelerating force would be fine for a long-travelling probe if this force could be kept constant. Unfortunately solar pressure reduces drastically as you move towards the borders of our solar system, which reduces options for this otherwise truly beatiful way of travelling.

  13. #13 thoughtcounts Z
    August 2, 2008

    I remember a homework problem about this in my freshman E&M class — a laser pointed at a mirror while sitting on a frictionless table, how fast does it move backwards, or something. It helped convince me that I had picked the right major. Physics is awesome. :)

    Glad to see you’re on ScienceBlogs!

  14. #14 Torbj�rn Larsson, OM
    August 2, 2008

    Another nice toy vs photon momentum is the old reflective/blackened vacuum propeller thingy. (can’t remember its name right now.)

    Oh, and I concur on the disuse of non-SI units, at least on a blog with international readership. Google is readily available for those with “special needs”. :-P

    The momentum thing p=mv actually still works for photons once you consider the relativistic mass instead of the rest mass.

    While that is technically correct, I believe the definition of “relativistic mass” has been depreciated since I did grad school. AFAIU “mass” is now always the invariant mass. (Maybe a topic for a physics blog post.)

    At least in the blogs; I have gotten nitpicked several times. So I’m now spreading the nit infestation. :-/

  15. #15 Dr
    August 2, 2008

    Uncle Al:
    > Distribution of force/area for light pressure on a
    > taut (but stretchable – square kilometers) mirror
    > membrane bulges into a concave mirror on the lighted
    > side. Don’t have your capsule or lines at the focus
    > or cutting a caustic. Poof!

    No kidding! But the traditional boat sail analogy can be misleadling. Don’t put your ship/capsule on the sunward side at all. Let the sail push the rest of the assembly ahead of it, right?

  16. #16 Stagyar zil Doggo
    August 2, 2008

    Can a solar sail beat upwind?

    UncleAl: what’s the speed of ‘sound’ for solar wind? Also, the solar constant at Earth orbit you mention as 1368 W/m^2 – is this just power from EM radiation, or does it include the ‘solar wind’?

  17. #17 Odysseus
    August 2, 2008

    Torbjörn: I suppose you meant a radiometer like the one on my window sill. Unfortunately it only happens to be a thermodynamic engine which works because of the pressure of the remaining gas, not directly due to the photon momentum. Lovely toy, though.

  18. #18 Uncle Al
    August 2, 2008

    Engineering rigidity into large aspect ratio hugely adds mass. Waffle geodesic hemisphere, tensegrity, or a Hoberman ring as you will, solar sails only configure in spontaneous tension. If solar wind adsorbs to the sail, 0.074 mg/cm^2 is an added tonne of mass for the one pound thrust case.

    A rigged NASA demo is not technology. Scaling of non-linear effects is brutal. Tank mixing energy varies as [(impeller diameter)^5][(rotation speed)^3]. A stir bar in a flask does not model 10,000 gallons of wort in a Budweiser vat. A small solar sail over a couple of days is not a big one over a few years. TANSSTAAFL

  19. #19 Notkieran
    August 2, 2008

    Actually, one very exciting approach to the solar sail issue that I came across was to coat the sunward side with an ablative paint that absorbs sunlight. As the paint absorbs the light, it vaporises. With correctly shaped “cells” to contain the paint, the thrust can be directed more efficiently than with a simple sail.

    Uncle Al:

    Tanstaafl is a completely meaningless concept when it comes to physics, because EVERYTHING in useful physics is a free lunch– you take energy and resources that were previously useless and make it useful, and that means that from the perspective of the person who is not familiar with the concept at hand, energy and resources appeared apropos of nothing. If you were to believe that there ain’t no such thing as a free lunch, then you would have to reject all solar cell technology.

    Come to think of it, you could not have a barbecue, because the energy you, personally, put in, is far less than the energy you get out.

    I went into some detail on my diary a while back; the entry is here (I’ve not had much success with links here on scienceblogs, so I’ll just paste the address in:

    http://www.opendiary.com/entryview.asp?authorcode=A434612&entry=21525

    Tanstaafl is, ultimately, a defeatist attitude when speculating on a new concept; there’s a reason why the rules of brainstorming are what they are.

  20. #20 NuHorizons
    August 3, 2008

    Pounds? Miles? I thought science used the SI system.

  21. #21 anon
    August 3, 2008

    These things work much better on the micro-scale, and don’t rely on the sun for photons, use a big photon-gun like a 10 W laser!

    I suggest you post and teach about how optical tweezers and atom-traps work next! For optical tweezers you can do it using ray-optics (large objects), or the Rayleigh approximation (small objects), but what most people use and trap are particles close to the wavelength in size, so a Mie theory is required.

  22. #22 Matt
    August 3, 2008

    Sorry, I shall not give in to metric snobbery. ;) While I work essentially exclusively in metric, I think the English units are perfectly fine for talking about concepts from a popular standpoint.

  23. #23 Uncle Al
    August 3, 2008

    EVERYTHING in useful physics is a free lunch

    Physics is a testable mathematical model of observed reality. A “free lunch” depends upon who is riding and who is ridden.

    1) Time is homogeneous;
    2) Noether’s theorems;
    3) Mass-Energy is locally conserved: you cannot win.
    4) Second Law of Thermodynamics;
    5) Large Number Theorem;
    6) All machines are lossy: you cannot break even.
    7) (It never gets that cold – Third Law!)

    Like ISS FUBAR, a space sail only reduces to practice if it isn’t used. It’s a rigged demo, it doesn’t scale up. (Only a committee of royalty of the kingdom of idiots would orbit an elongated structure tangent rather than normal to the geoid. Physics tells us why.)

  24. #24 Hamsterpoop
    August 4, 2008

    Matt: “Sorry, I shall not give in to metric snobbery. ;) While I work essentially exclusively in metric, I think the English units are perfectly fine for talking about concepts from a popular standpoint.”

    But don’t you think that your audience will have a better grasp of metric units? Although velocities and distances are a bit easier to visualize in English units because of daily use, other quantities aren’t quite as easy. Besides, you started with Watts per squared meter!

    Anyway, I’m really enjoying your blog! Welcome to SciBlogs!

  25. #25 Notkieran
    August 4, 2008

    1) Time is homogeneous;

    Sorry, don’t see a problem or relevance. Perhaps you could explain why this prevents a free lunch.

    2) Noether’s theorems;
    3) Mass-Energy is locally conserved: you cannot win.

    Ah, I begin to see your problem. You assume that a free lunch means we have to CREATE energy and matter. I already said that gaining access to energy and matter which was previously unaccessible to us is, by definition, a free lunch. Take, for example, what I said about a barbecue fire; before and after the fire, the total amount of energy remains the same, but the _transformation_ of that energy does our cooking. If that’s not a free lunch FOR US, I don’t know what is.

    4) Second Law of Thermodynamics;

    That only applies to a closed system; the earth gets enough free energy to generate a Richter 12 earthquake every single day. Why do I consider it free? Because we do not have to work to make the sun provide energy.
    5) Large Number Theorem;
    Relevance? It’s like saying that the total amount of money in an economy is fixed and thus nobody can ever earn any money. Ever.

    6) All machines are lossy: you cannot break even.
    I have a solar-powered watch. I don’t have to pay for a battery. I count my energy ledger to be positive in my favour. Next.

    7) (It never gets that cold – Third Law!)

    Relevance?

    I agree that a rigged demo is not the same as a full-on project; look at Star Wars, for a start.

    I object to the term TANSTAAFL being used in physics as if it were some great insight, given that all engines make use of free lunches in making useless energy useful to us.

    Come on. Petrol is not useful until you burn it. The fact that we do not get more petrol back from burning it is immaterial; the fact that we can GET energy from burning petrol IS the free lunch, just as solar power is a free lunch.

    The entire UNIVERSE is the ultimate free lunch, or did you miss that?

  26. #26 Notkieran
    August 4, 2008

    Actually, let me sum up your argument and my argument:

    My argument: It is possible to get a free lunch, because you pick up something that was created somewhere at no cost to you, and you make use of it. For example, engines use potential energy– which is inherently useless– to do work.

    Your argument: It is impossible to get a free lunch, because SOMEONE has paid for it, somewhere. Thus, to you, engines are not examples of free lunches, because SOMETHING had to be done to create the fuel.

    Now that is patently absurd. It is like saying that when a distant relative dies and leaves a fortune to you with no strings attached, it is not a free lunch because that person earned it. Or that randomly winning the lottery is not a free lunch, because all the people who bought the tickets worked for their dollar.

    If I have misjudged your point of view, please explain to me how all the free energy entering the earth’s ecosystem via the sun is NOT a free lunch, please. And explain why if we can tap into that energy either directly or indirectly, how it is not a free lunch.

  27. #28 andy.s
    August 4, 2008

    Crap. I screwed up the link. Here it is: Gold

  28. #29 CCPhysicist
    August 4, 2008

    As Odysseus pointed out to Larsson, the device sometimes called a “radiometer” or “light mill” does not work on photon pressure. In fact, it turns the OPPOSITE DIRECTION to what you would predict from photon reflection and absorption.

  29. #30 Torbj�rn Larsson, OM
    August 5, 2008

    FWIW, catching up on old threads:

    @ Odysseus:

    Ah, right, thanks!

    So I was wrong, I learned that Crookes radiometer was evacuated, so no thermal engine explanation possible. But it seems it is only partially evacuated.

    @ CCPhysicist:

    In fact, it turns the OPPOSITE DIRECTION to what you would predict from photon reflection and absorption.

    Oh! Should have taken time to actually find one to observe, instead of accepting what seems to be physics folk tales.

    @ Matt:

    I think the English units are perfectly fine

    Perfectly fine where used. Doesn’t answer the international aspect though. (Or as noted, the aspect of the expected readership.) But it’s your blog, your units.

  30. #31 Liberal Atheist
    August 6, 2008

    Sorry, I shall not give in to metric snobbery. ;) While I work essentially exclusively in metric, I think the English units are perfectly fine for talking about concepts from a popular standpoint.
    From a popular standpoint? The world is using SI units. How many countries actually use the Imperial units? The USA and who else? The most “popular” system is the SI system, and therefore that’s what you should use. Unless you only want readers from the USA. I’m not at all surprised.

  31. #32 Liberal Atheist
    August 6, 2008

    I’ll try again then.

    Sorry, I shall not give in to metric snobbery. ;) While I work essentially exclusively in metric, I think the English units are perfectly fine for talking about concepts from a popular standpoint.

    From a popular standpoint? The world is using SI units. How many countries actually use the Imperial units? The USA and who else? The most “popular” system is the SI system, and therefore that’s what you should use. Unless you only want readers from the USA. I’m not at all surprised.

  32. #33 Matt Springer
    August 6, 2008

    The most “popular” system is the SI system, and therefore that’s what you should use.

    I’m required to use the most popular system? Well, I suppose this site will have to go on hiatus while I learn Mandarin Chinese. I also thought that liberals were supposed to be tolerant of other cultures, linguistic systems, minority views, etc. ;)

    The fact of the matter is that the ScienceBlogs readership is overwhelming American. In a distant second place is the UK, which uses metric but (obviously) understands English units. The entire rest of the EU readership combined is not even as large as the UK readership because this site is mostly written in English. And since I’m an American as well it’s doubly convenient for me to occasionally take advantage of most people’s daily familiarity with English units.

    But metric is the system of physics and of most of the rest of the world, so what I normally do is use both. Metric for the actual formal answer, and sometimes English for comparisons to everyday situations. For instance, today’s (08/06/08) post will be a little more formal in its calculation and will use metric exclusively. This is what I consider to be an ideal compromise.

  33. #34 Dunc
    August 6, 2008

    Possibly a bit late to this one, but never mind…

    I have a question that’s been bugging me about solar sails for ages: what about the fact that light pressure falls off over distance? Every time I see the idea discussed, this is never mentioned…

    Oh, and the units known in the US as “English units” aren’t actually English (or rather, Imperial) units. Several of the units of volume (at least) are different, although they have the same names. For a UK reader, this is even more confusing than SI units. Plus, many UK readers under the age of about 40 are no longer particularly familiar with Imperial units. I’m 35, and Imperial units were never used at all during my schooling – I always have to convert them to SI units to make any real sense of them. Sure, I know what an inch, a foot, a yard, a pint and a pound look like, but I really have to think about it to remember how many ounces are in a pound, and I haven’t a clue how many yards are in a mile. I do know that a mile is approximately 1.6km though…

  34. #35 Metro
    August 6, 2008

    My first visit here. It’s a bit high-flown for me, as my science education peaked at grade 10 or so. However, I’m interested in the idea of the solar sail, and I have a question:

    That four pounds of force is continuous, so it would produce acceleration in the vacuum of space for as long as the light shone on it, am I right?

    Does that mean we could create a one-gee continuous-boost sail simply by scaling up?

    I have to say, the idea excites me like Christmas does an eight-year-old.

  35. #36 Matt Springer
    August 6, 2008

    Yes it would if the light kept shining at the same intensity, but as you get farther from the sun less light will be shining on it. So the acceleration will decrease just because you get farther away, sadly.

    But you can still end up some pretty tremenedous net speeds! In fact, I’ve got a post coming online later this afternoon about that.

The site is currently under maintenance and will be back shortly. New comments have been disabled during this time, please check back soon.