Author Topic: A more realistic 0.001c with a Solar Sail  (Read 15377 times)

Offline scienceguy

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A more realistic 0.001c with a Solar Sail
« on: 11/24/2011 07:10 pm »
Ok so I did some research related to this post:

http://forum.nasaspaceflight.com/index.php?topic=22582.0

In that post, I suggested an aluminum sail 1 nm thick. As hop pointed out, 1 nm is too thin to reflect anything, and as mlorrey pointed out, aluminum melts at too low a temperature to be useful for this application. Thus, I readjusted the calculations for titanium.

Titanium reflects 20% at 5 nm thickness (Hass, 1952), and titanium has a much higher melting point than aluminum (1668 C as opposed to 660 C). However, titanium also has a low density like aluminum. mlorrey had also pointed out a paper where beryllium was used for a solar sail, because beryllium has even lower density (I did not find a paper on reflectance of beryllium at small thicknesses).

In this calculation I assume the titanium sail can pass within 0.1 AU of the sun without melting. If anyone knows different, please say so. This calculation also has the sail only used up to 10 AU.

Thus, redoing the calculations with 5 nm thick titanium:

Assuming payload is 10^5 kg:

Mass of sail:

5 x 10^-9 m x 10^10 m^2 = 50 m^3

50 m^3 x (4.5 x 10^3 kg/m^3) = 2.25 x 10^5 kg

Thus total mass of spacecraft is 2.25 x 10^5 kg + 1 x 10^5 kg (payload) = 3.25 x 10^5 kg

(from Jim Davisí outline in that same thread):

Radiation pressure:

k = k0 * R0^2 / x^2

where

k0 = radiation pressure at earth orbit 4.6 x 10^-6 Pa
R0 = radius at earth orbit (1 AU) 1.5 x 10^11 m

For constant mass

F = m * dv/dt

where

m = 3.25 10^5 kg

but

F = k * S

where

S = 10^10 m^2

So

m * dv/dt = S * k0 * R0^2  / x^2

and since v = dx / dt

v * dv = S * k0 * R0^2 / m / x^2 * dx

Integrating the left side between 0 and Vfinal and the right side between .1 * R0 and 10 * R0 and solving for Vfinal gives

(I added a factor of 0.2 to account for less reflectance at small thicknesses)

Vfinal = Sqrt(2 * S * k0 * R0 / m * 9.9 * 0.2) = 289 000 m/s

or Vfinal = 0.001 c

If the sail could pass closer to the sun, the final velocity would be higher. Of course, you can't pass so close that the sail melts.

Reference

Hass, G. (1952) Preparation, properties and optical applications of thin films of titanium dioxide. Vacuum 2(4):331-345
e^(pi*i) = -1

Offline 93143

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Re: A more realistic 0.001c with a Solar Sail
« Reply #1 on: 11/24/2011 10:36 pm »
Vfinal = Sqrt(2 * S * k0 * R0 / m * 9.9 * 0.2) = 289 000 m/s

VASIMR with hydrogen propellant will do that with a mass ratio of less than 3.

Offline tnphysics

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Re: A more realistic 0.001c with a Solar Sail
« Reply #2 on: 11/25/2011 12:57 am »
What would be the power source?

Offline 93143

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Re: A more realistic 0.001c with a Solar Sail
« Reply #3 on: 11/25/2011 01:52 am »
Does it matter?  Solar and fission are both options, though if you're heading away from the sun long enough you'd probably want fission.  If aneutronic fusion works out, we could use that.

Of course, with fusion we'd have the option of using directed ash, for a specific impulse in the general vicinity of a million seconds.  The same mass ratio would get you to about 2-3% of the speed of light...  but as this is not strictly current technology, it's not really a fair comparison...
« Last Edit: 11/25/2011 02:01 am by 93143 »

Offline Solman

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Re: A more realistic 0.001c with a Solar Sail
« Reply #4 on: 11/25/2011 10:31 pm »
Mass of the sail can be further reduced by cutting holes smaller than visible light in the sail reflector - maybe by a factor of ten or so.
 If I remember correctly, beryllium was proposed for Star Wars orbiting mirrors for ground based lasers. Maybe there's something on Beryllium reflectance there.

Offline clongton

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Re: A more realistic 0.001c with a Solar Sail
« Reply #5 on: 11/26/2011 12:02 am »
93143- please be careful to not unintentionally draw the discussion off topic.
Stick to the sail please.
Chuck - DIRECT co-founder
I started my career on the Saturn-V F-1A engine

Offline 93143

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Re: A more realistic 0.001c with a Solar Sail
« Reply #6 on: 11/26/2011 01:04 am »
Don't worry; I'm done.  I was just trying to provide a reference point for the delta-V...

Offline scienceguy

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Re: A more realistic 0.001c with a Solar Sail
« Reply #7 on: 11/26/2011 01:26 am »
Mass of the sail can be further reduced by cutting holes smaller than visible light in the sail reflector - maybe by a factor of ten or so.
 If I remember correctly, beryllium was proposed for Star Wars orbiting mirrors for ground based lasers. Maybe there's something on Beryllium reflectance there.

Mass of the sail can be further reduced by a factor of 10? That would up the final velocity by 3 times!
e^(pi*i) = -1

Offline Tass

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Re: A more realistic 0.001c with a Solar Sail
« Reply #8 on: 11/26/2011 11:20 am »
Mass of the sail can be further reduced by cutting holes smaller than visible light in the sail reflector - maybe by a factor of ten or so.
 If I remember correctly, beryllium was proposed for Star Wars orbiting mirrors for ground based lasers. Maybe there's something on Beryllium reflectance there.

Can it? If the material is already so thin that it has significant transmittance, I would think that removal of material would further increase transmittance and reduce reflectance. Basically I'd think that as long as the holes are on a scale shorter than the wavelength then the light does not see the structure but only that there is less material reflecting. So making holes and making it thinner would have the same effect.

Of course if you are limited by technology to something of greater thickness then holes can make sense. For reflecting microwaves a mesh is probably easier to handle and produce than a thin uniform foil.

Correct me if I am wrong, I have not actually done any electrodynamic calculations to see if concentrating the material into wires could give a higher reflectance than having it spread out. 

Offline Solman

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Re: A more realistic 0.001c with a Solar Sail
« Reply #9 on: 11/30/2011 12:18 am »
Mass of the sail can be further reduced by cutting holes smaller than visible light in the sail reflector - maybe by a factor of ten or so.
 If I remember correctly, beryllium was proposed for Star Wars orbiting mirrors for ground based lasers. Maybe there's something on Beryllium reflectance there.

Can it? If the material is already so thin that it has significant transmittance, I would think that removal of material would further increase transmittance and reduce reflectance. Basically I'd think that as long as the holes are on a scale shorter than the wavelength then the light does not see the structure but only that there is less material reflecting. So making holes and making it thinner would have the same effect.

Of course if you are limited by technology to something of greater thickness then holes can make sense. For reflecting microwaves a mesh is probably easier to handle and produce than a thin uniform foil.

Correct me if I am wrong, I have not actually done any electrodynamic calculations to see if concentrating the material into wires could give a higher reflectance than having it spread out. 

 Such calcs are beyond me - I was just basing that on mesh antennas for microwaves and radio waves. It should work at visible light wavelength scale just as well. Mesh in mesh antennas is much thinner than the wavelength of what it reflects and the mesh is very thin compared to the antenna's overall size and they work quite well.
 I would guess that the mesh would be best used to make the sail effectively thicker and therefore more reflective for the same mass. One benefit of greater reflectivity would be less radiant heat absorbed from the Sun allowing a closer approach and therefore higher final velocity.
Steve

Offline scienceguy

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Re: A more realistic 0.001c with a Solar Sail
« Reply #10 on: 11/30/2011 08:45 pm »
You know how a microwave oven has a mesh on it that lets visible light through but not microwaves? What if you had a second sail made of tungsten in between the first sail and the sun except that the second sail has a mesh in it that blocks infrared radiation but lets visible light through. This second sail in between the first sail and the sun would have a much higher melting point and yet would not crash into the first sail because it's heavier. Thus you could have both sails pass closer to the sun.
e^(pi*i) = -1

Offline Solman

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Re: A more realistic 0.001c with a Solar Sail
« Reply #11 on: 11/30/2011 11:04 pm »
You know how a microwave oven has a mesh on it that lets visible light through but not microwaves? What if you had a second sail made of tungsten in between the first sail and the sun except that the second sail has a mesh in it that blocks infrared radiation but lets visible light through. This second sail in between the first sail and the sun would have a much higher melting point and yet would not crash into the first sail because it's heavier. Thus you could have both sails pass closer to the sun.

 I love that ides. The problem might be getting the two sails to fly formation with each other. The shielding sail might have to be larger and lower in mass to keep up.
 Borrowing a page from Issac Kuo, the momentum this sail or perhaps dozens of sails have may be transferred by impact to a larger spacecraft that could be gently accelerated and need not approach the Sun.
 Makes me wonder just how fast these sails can get. Could they get to 3% light speed?

Steve

Offline Proponent

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Re: A more realistic 0.001c with a Solar Sail
« Reply #12 on: 12/01/2011 02:16 am »
Preventing the infrared radiation from striking the sail will reduce the heating of the sail but won't prevent it and, at the same time, will reduce the thrust produced by the sail.

We commonly associate infrared with heat, but that's only because objects near room temperature glow principally in the mid-IR.  There's nothing special about infrared and heat: infrared is simply light in a certain range of wavelengths.  What matters in determining the sail's temperature is how much radiation (at all wavelengths) it absorbs.  The way to keep the sail cool is to make it as reflective as possible at the wavelengths of the radiation striking it and as emissive as possible (i.e., non-reflecting, which we call "black" in the visible range) at the longer wavelengths at which it itself radiates (glow).

Offline Lampyridae

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Re: A more realistic 0.001c with a Solar Sail
« Reply #13 on: 12/01/2011 06:59 am »
I think scienceguy knows that. What he's proposing is a screen to keep the IR portion from impinging on the sail, which may have low IR reflecting properties.

Lithium becomes transparent at high temps, but beryllium has been proposed as a good sail material.

Using an X-ray laser to heat the tungsten sail (thicker and with no holes) would make a great blackbody radiation source to drive the sail at interstellar distance (no need for a 1000km diameter fresnel lens).

Offline scienceguy

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Re: A more realistic 0.001c with a Solar Sail
« Reply #14 on: 12/03/2011 06:01 pm »
Anybody know the temperature at which 5 nm thick titanium becomes transparent to radiation?
e^(pi*i) = -1

Offline scienceguy

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Re: A more realistic 0.001c with a Solar Sail
« Reply #15 on: 01/15/2012 01:00 am »
I just wanted to update this thread. After more research and calculations, I found that it would be very difficult to exceed 1/1000 the speed of light with a solar sail, no matter what metal one used. I looked at tungsten, and although you can pass closer to the sun because of its higher melting temperature, tungsten is so dense that it pretty much cancels the benefit of passing closer to the sun.

Titanium seems optimal, but its melting point is about half that of tungsten, so you can't pass as close to the sun as tungsten, so you can't get much faster than 1/1000 c. The only other option was mentioned in this thread: punch holes in the sail to make it lighter. There were some doubts as to this being feasible.
e^(pi*i) = -1

Offline scienceguy

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Re: A more realistic 0.001c with a Solar Sail
« Reply #16 on: 05/10/2012 04:47 am »
Upon further reflection, I realized that the paper I quoted (Hass, 1952) uses titanium dioxide, not titanium. This makes a big difference. Titanium dioxide has a higher melting point and thus can pass closer to the sun without melting.

The following calculation summarizes this:

T=Ts*(Rs/(D*2))^0.5

where Ts=average sun temperature. approx 5800K.

Rs=sun radius
D=average distance sun-planet
T=average planet temperature.

That equation can be rearranged to give the distance at which a particular temperature occurs:

D = (Ts^2/T^2)*(Rs/2)

Which, for the melting point of titanium dioxide, gives:

D = (5800 K/1570 K)^2 * (7 x 10^8 m/2) = 5 x 10^9 m or 0.03 AU

Thus, redoing the calculations with 5 nm thick titanium dioxide:

Assuming payload is 10^5 kg:

Mass of sail:

5 x 10^-9 m x 10^10 m^2 = 50 m^3

50 m^3 x (4.2 x 10^3 kg/m^3) = 2.1 x 10^5 kg

Thus total mass of spacecraft is 2.1 x 10^5 kg + 1 x 10^5 kg (payload) = 3.1 x 10^5 kg

Radiation pressure:

k = k0 * R0^2 / x^2

where

k0 = radiation pressure at earth orbit 4.6 x 10^-6 Pa
R0 = radius at earth orbit (1 AU) 1.5 x 10^11 m

For constant mass

F = m * dv/dt

where

m = 3.1 x 10^5 kg

but

F = k * S

where

S = 10^10 m^2

So

m * dv/dt = S * k0 * R0^2  / x^2

and since v = dx / dt

v * dv = S * k0 * R0^2 / m / x^2 * dx

Integrating the left side between 0 and Vfinal and the right side between 0.03 * R0 and 10 * R0 and solving for Vfinal gives

(I added a factor of 0.2 to account for reflectance at thickness of 5 nm)

Vfinal = Sqrt(2 * S * k0 * R0 / m * 33.2 * 0.2) = 540 000 m/s

or Vfinal = 0.002 c or 1/500 c

Thus the final velocity of the craft is about twice that if just titanium is used, because titanium dioxide has a higher melting point and is less dense.

Reference
Hass, G. (1952) Preparation, properties and optical applications of thin films of titanium dioxide. Vacuum 2(4):331-345
e^(pi*i) = -1

Offline Lampyridae

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Re: A more realistic 0.001c with a Solar Sail
« Reply #17 on: 05/10/2012 10:54 am »
I was just looking at this and thinking of TixOy and crystalline materials that look white because they simply refract the light back. A sail coated with spherical micro- or nano-diamonds could do just that and have high temps (wavelength effects excluded).

Offline scienceguy

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Re: A more realistic 0.001c with a Solar Sail
« Reply #18 on: 05/10/2012 04:53 pm »
I realized for the melting point of titanium dioxide I subtracted 273 from 1843 degrees Celsius instead of adding to get the temperature in Kelvin. If you add 273 and get the proper 2116 K for the melting point of titanium dioxide, you get a final velocity of 7.0 x 10^5 m/s, or 0.0023 c. This is only slightly higher, but worth noting.
e^(pi*i) = -1

Offline Lampyridae

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Re: A more realistic 0.001c with a Solar Sail
« Reply #19 on: 05/10/2012 08:08 pm »
An inflated lenticular sail would better reflect the light for thrust... but it still wouldn't be optimal.

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