Author Topic: The V prize  (Read 30812 times)

Offline Tom Ligon

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Re: The V prize
« Reply #20 on: 07/03/2007 08:36 pm »
Sorry for being so vague, but without my hands on an atmospheric model for high altitudes, all I could do is wave my hands.

Alas, the guy in the cube across from me was just discussing the other extreme of the problem, and clued me in to this:

http://www.aerospaceweb.org/design/scripts/atmosphere/

So now I guess I have to calculate how much of the flight will actually involve hypersonic aerodynamics.  Urrrh!  The trouble I make for myself!

The horizontal velocity required will, of course, be a seriously high fraction of orbital velocity.

I did attempt a related calculation once, so I have some idea of what is involved.  Fraction of orbital velocity reduces the weight of the aircraft and so the lift that must be achieved, but at the penalty of drag.  Obviously you need to clear most of the atmosphere to make this thing viable, so most of the trajectory needs to be almost entirely ballistic.  Then the question becomes, high arc like an ICBM, or a flat arc but higher velocity?  Then how much, and what are the aerodynamics of the end of flight?

Because you do not need to achieve sustained orbit, and it would be good to stay clear of orbit for the traffic issue, it probably is permissible to keep the trajectory low enough that drag would prohibit sustained orbits, but high enough that the drag is ALMOST negligible for most of the flight.  Thus, my inclination to think that this thing will never be totally clear of hypersonic considerations.  A good atmosphere model will be needed to determine where the viable range of trajectories lies, and then attempt to find the best trade-off.


Offline meiza

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Re: The V prize
« Reply #21 on: 07/03/2007 08:57 pm »
With the favorable assumptions of infinite T/W and no drag, a 100 km vertical hop is 1.5 km/s. In reality, more delta v is needed of course.

The 6000 km arc requires probably a very high apogee in the thousand-km class or then very high speed. The high apogee route most probably requires less total delta v. (Sounding rockets can reach 1000 km suborbital altitudes.)
I don't think hypersonics will help much in this - your lift to drag would have to be phenomenal if you wanted to have much advantage of it. Perhaps you could use a scramjet?

Think of the trajectories as elliptical orbits.
A high ballistic lob one has perigee inside earth (very near the center of earth), while the apogee is quite high, radius of earth + n*1000km from earth's surface.
A low trajectory needs to have both somewhat high apogee and perigee: r_earth + n*100 km from earth's surface.
Taking into account the 7000 km radius of earth, it's probably cheaper to have a highly elliptical orbit.

Offline Tom Ligon

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Re: The V prize
« Reply #22 on: 07/03/2007 09:58 pm »
I'm biased by my former calculations, which was a hypersonic jet.  I deliberately kept it in the fringes of the atmosphere, and the key was utilizing enough air for thrust to offset the drag.  At sufficiently high velocity, the lift/weight part of the problem diminished.

I have not looked into the energy needed to achieve enough delta-V for a flatter trajectory, but artillery considerations suggest it does take more energy to go flatter.  Yet, we achieve that going for LEO, so it is not out of the question.

Offsetting the high energy cost of a flat trajectory is the question of re-entry.  Without actually doing any calculations, my instinct says an ICBM near-vertical re-entry will tend to be abrupt.  I'm trying to picture hitting the atmosphere vertically at several miles a second, with about 99% of the atmosphere in the last 18 miles, and increasing in density exponentially.  We have never brought people back like that.  From LEO, we come back tangentially.  So I'm thinking the market potential (already tenuous at best) may favor not crushing the passengers.  An ICBM does not have to slow much on re-entry.

I think re-entry will probably need to look a lot like a shuttle re-entry (a tad slower) and will take almost as far (1500 miles of significant fireball stuff?)

It also occurs to me that a tran-Atlantic flight probably is one of the least economical applications. The difference in energy needed to do a flat trajectory across the Atlantic is almost the same as that required to go any place on a great circle from the launch site.   As has been mentioned, it would be near orbital velocity.

Offline meiza

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Re: The V prize
« Reply #23 on: 07/05/2007 10:17 am »
So, the problem of re-entry favors low trajectories which makes the delta v requirements even more drastic. The total requirements might be 80% from orbital launch velocity by then.
3000 km range IRBM:s required about 5 km/s on an efficient high ballistic trajectory.
And we are talking about 6000 km with the V prize...

I think Rocketplane (not sure if I remember correctly) guys said that orbital services will come before point to point.

Offline Tom Ligon

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Re: The V prize
« Reply #24 on: 07/05/2007 04:00 pm »
That sounds like a reasonable assessment.

In my judgment, there is no question that such a project can be accomplished from a technical standpoint.  We can get into orbit and back, so any suborbital version can be done.  The question is, can small-scale efforts, with X-Prize-like incentives and organizations, do it at a tolerable cost.  And the BIG question is, WHY?  

The Rocketplane guys sound like they've asked the same question (one would hope!), and concluded that LEO is the more immediate payoff.  The real question is one of business economics.  A demo flight would be very entertaining, as was Lindberg's crossing of the Atlantic.  Airlines needed a good business model to make it meaningful.

Of course, the fact Lindberg had done it was a valuable publicity tool, and they hired him as an airline executive.

The Concord was never really successful from a business standpoint.  How much extra is it worth to get to Europe in 1 hour instead of 10?  Especially if you have to wait a couple of days to catch an infrequent flight, instead of catching one from Dulles, available every couple of hours?   I would expect this scheme would be attempted first on either a charter basis or as an air-express service for very high-value time-critical material, with lots of standby time and depending on being able to launch quickly on demand.  And maybe it would work ... FedEx succeeded when the experts said it would never work.

But, to steal an idea from a cartoon on the bulletin board at the Va Tech Aerospace Engineering department back in the 70's, at least the thing will be so fast they'll be able to eliminate the restrooms.

Offline Tom Ligon

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Re: The V prize
« Reply #25 on: 07/05/2007 05:23 pm »
Looking at the rationale for doing this particular stunt, maybe it is worthwhile for the following reasons.

1)  We already have folks going into orbit ... been there, done that.

2)  Demonstrating the suborbital point-point hop has been blabbered about for decades, but never demonstrated as a viable means of transporting anything but warheads.  Without the demonstration to generate some data as to what can reasonably be done, nobody is likely to think seriously about a business plan.

3)  Some technological innovation is required due to a) the fact that people are not warheads and b) the X-Prize mentality of finding a way to do it cheaper than NASA does it.

4)  In some ways, this would be easier for a small outfit to do.  Rocket propulsion is straightforward ... it is only rocket science, fuel and oxidizer will be cheap compared to the rest of the effort, and the requirements will be SOMEWHAT less stringent than actually achieving LEO.  But the craft will not require life support for days in space.  It may not be much fancier than a fighter or business jet.  

I think it WILL be a significant departure from Space Ship One.  Maybe more like LKS, the "smaller-cheaper" alternative shuttle design once proposed as an alternative to the US STS and Soviet Buran?  Hypersonic re-entry vehicle on top of a conventional booster?  Or maybe launched from a jet using improved, possibly staged, hybrid engines or even scramjets plus rockets?

The goal of these prizes is to induce people to try something new.  Regardless of the eventual viability of the concept, that alone is worth the comparatively modest effort compared to the mainstream NASA space program.


Offline Tom Ligon

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Re: The V prize
« Reply #26 on: 07/05/2007 06:33 pm »
Oh, this is easier than calculating.  Look it up.  NASA's light-duty description of shuttle re-entry:

http://www.spaceflight.nasa.gov/shuttle/reference/shutref/events/entry/

"The entry phase of flight begins approximately five minutes before entry interface, which occurs at an altitude of 400,000 feet. At EI minus five minutes, the orbiter is at an altitude of about 557,000 feet, traveling at 25,400 feet per second, and is approximately 4,400 nautical miles (5,063 statute miles) from the landing site."

That's saying they hit the atmosphere at 76 miles at 4.81 miles a second or a little more, and it takes 5000 miles to slow down.  So the V-Prize hypersonic re-entry with a flat trajectory, re-entry should be less than half the hop, so 3000 miles max.

It goes on to say they drop to 1700 mph at 83000 ft (in line with my guestimate: my usual figure of merit is mach 3 at 80,000 ft as about the highest dynamic pressure to assume you can design for), 59 miles from the landing site.

The launch profile would probably be mostly nearly straight up until at least 100k ft, to reduce drag as much as possible until most of the atmosphere is below, keeping 1/2 ro v^2 well below the desired max Q as much as possible (design point 83000 ft at about 1700 mph).  At some high altitude, the craft must begin to pitch over and acquire horizontal velocity.   I'd guess the profile will want to be above 76 miles for at least half the flight distance, and in that span the trajectory must be ballistic.  At the end of the ballistic phase, re-entry occurs and the craft seeks to use up the excess velocity making lift and drag.  My assumptions are, rather than decelerating fast, attempt to generate lift to stay higher to scrub off speed gently.  This is not just a "glide" from high altitude, it presumes there is a huge excess of momentum to get rid of.  Thus, a couple of thousand miles of hypersonic flight at the end of the mission is not unreasonable.

Offline meiza

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Re: The V prize
« Reply #27 on: 07/06/2007 02:42 pm »
But your downrange numbers look big because the space shuttle enters at 8 km/s at a close to horizontal angle. A point to point craft can't be like that. (It'd require as much delta v as an orbital craft then, defeating the whole purpose.) "Hitting the atmosphere" is not very accurate either.

First of all, let's use some units that are intercompatible to look at the problem, and not the whole miles, feet and nautical miles horridities.

There is a figure at islandone.org:
http://www.islandone.org/Launch/boron-sharp-article_files/sts_reentry_trajectory.gif
That shows that from re-entry start at 8 km/s (orbital velocity) it takes roughly 1000 seconds (17 minutes) to brake to 5 km/s at 60 km altitude and another 800 s (13 minutes) to touchdown. The first part is done almost belly first.

If we generously assume the entry velocity of the speculated point to point traveling craft to be 5 km/s and to have the same aerodynamic characteristics as the shuttle (which is favorable too), we can use the shuttle data and estimate the traveled distance from the velocity integral which is pretty much a triangle between points of 5 km/s at 1000s and 0 km/s at 1600 s, ie 2.5 km/s for 600 s = 1500 km.

So it doesn't help that much, the entry glide is about one quarter of the whole trip if you do very generous velocity assumptions. You'd need horizontal velocity of 5 km/s after the 4500 km ballistic arc for that. If you come in slower, you glide less (or you have to have a different craft, and then the whole thing becomes slower too.)

There are new very high heat tough materials like SHARP which could probably make it possible to have higher hypersonic L/D which would extend range. I don't know if they could triple it though.

But orbiting a stable Apollo shape with an ablative heat shield starts looking simple very quickly, when compared to all this...

Offline meiza

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Re: The V prize
« Reply #28 on: 07/06/2007 03:17 pm »
The sponsors of Virginia's spaceport could perhaps get some better prize that was more easily achievable. It could be done with less money too, and still generate publicity. A 300 km vertical unmanned hop perhaps. (Or is the population density too high, requiring all launches to be towards east?)

Offline meiza

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Re: The V prize
« Reply #29 on: 11/30/2007 03:17 pm »
http://spaceports.blogspot.com/2007/11/v-prize-challenge-to-commercial-space.html
They seem to be pressing on. The rules are still not published.

If it's one hour for a distance of 6000 km, I'd class that as umm... somewhat ambitious. Air breathing is probably out, and probably gliding too leaving a ballistic ten thousand km high suborbital hop.

Offline Lampyridae

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Re: The V prize
« Reply #30 on: 12/02/2007 06:58 am »
For a transatlantic suborbital hop, you need close to orbital deltaV, that much is true. What is different, though, is that it's probably just low enough to avoid staging and the consequent R&D costs for either expendable or reusable stages. 4kps can be had from a LH2/LOX engine with about 2/3 of mass is fuel, leaving plenty for airframe.

High L/D numbers are key... at hypersonic speeds, lift is a much simpler thing to calculate as it becomes more Newtonian. You could glide quite a long way if you wanted to.

Offline meiza

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Re: The V prize
« Reply #31 on: 12/02/2007 07:54 pm »
If your distance is 6000 km, you would have to glide over 3000 km at least.
Given the very favourably assumed altitude of 50 km from where you could start gliding, this gives a slope of 1:60.
Only the best modern sailplanes can attitude such L/D to glide at 1:60. And they for sure are very low speed vehicles with absolutely subsonic flow everywhere and very minimized drag.

Further, if we assume the boost took 15 minutes, there's 45 minutes of time for this 3000 km glide.
That results in a speed of over 4000 km/h or 1.1 km/s. (assume no slow speed portion near the landing field!).
That's about Mach 4 at 10 km height. (35,000 ft).

We can immediately see that the resulting glider design is entirely unrealistic.
The atmosphere is just far too thin, less than 50 km. Gliding is useless over such multi-thousand kilometer distances.

Offline Lampyridae

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Re: The V prize
« Reply #32 on: 12/03/2007 01:52 am »
The Germans looked at using winged V2s to attack the US. The two-stage A9/A10 would have had an apogee of 300km and a range of 5000km. ICBMs won out over winged designs in the Cold War because they were faster and could not be intercepted.

http://www.project1947.com/gfb/a-9.htm

L/D is Lift over Drag, meaning the rate at which your velocity is being chewed away. High L/Ds are important for subsonic aircraft because they travel much more slowly. A 10 tonne hypersonic glider with an L/D of 10 experiences 10KN of drag in order to stay airborne, and is decelerating at about 1ms2. From Mach 3 to zero at this rate takes approximately 1000 seconds, assuming L/D stays constant (it doesn't). Note that altitude stays constant if L = Weight. Altitude can be traded for velocity, increasing the range.

At high Mach, L/D numbers are low but research shows that numbers as high as 12 are possible (I chose 10 for ease). The atmosphere does not disappear at 50km. It is very real, and at Mach 10 or so it is perfectly thick enough to provide lift at the given speed.

This is a crude approximation, but it will serve to illustrate the point. Real glide ranges are a pain in the butt to work out, and my textbook is in another country.

Mach 10 time to zero speed: 3000s (L/D = constant 10)
Range with zero drop: 4500km

Offline meiza

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Re: The V prize
« Reply #33 on: 12/03/2007 02:15 am »
Well, the german craft never flew now did it? They had no understanding of hypersonic aerodynamics (even supersonic stuff was weird back then!). The winged A-4's wings fell off in a test for example... So I wouldn't take the performance figures very seriously.

Blunt bodies were invented later and they have worked at hypersonic speeds without getting destroyed. As have the ablative cones for ICBM:s and the relatively blunt space shuttle and other smallish wings and lifting body shapes...

Glide path depends on L/D and speed depends on mass. And I don't believe in high hypersonic L/D. Show me otherwise, and I'm happy!

As for ramjets producing thrust for increasing distance, I believe the state of the art was reached in the 60:s to go up to Mach 4.5 with Bomarc. Maybe Mach 6 could be possible, I don't know. I haven't looked at the fuel requirements but they are quite dependent on drag. Beyond that it's a scramjet certainly, something extremely hard to make work.

Offline Lampyridae

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Re: The V prize
« Reply #34 on: 12/03/2007 03:20 am »
Yes, but the basic L/D versus speed equation holds.

L/Dmax = 4(M + 3)/M

Designs have been formulated that surpass this. Although L/D 10 at Mach 10 is unrealistic, and 12 probably impossible, 8 is possible and 6 has already been achieved (by things that actually fly). X-15 managed to have a range of 500km while not being a very high L/D design (maybe 2.5)


Offline meiza

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Re: The V prize
« Reply #35 on: 12/03/2007 02:48 pm »
So L/D = 4 + 12/M
At Mach 6 that would be 4+2=6.
Flying at constant altitude, L=mg meaning D=mg/6.
If we assume a 30 ton craft, the thrust needed would be 5 tonnes or 50 kN.
With a hydrocarbon ramjet with an ISP equivalent of 1800 s we get a fuel mass flow of 3 kg/s to have the thrust.
45 min = 2700 s so total fuel used would be 8 tonnes.
So perhaps when starting the cruise, the craft is 34 tonnes and when near the destination, 26 t.

But this is still too slow.
Mach 7 => L/D = 5.7 => F/g=5.2 t => mdot= 3 kg/s so the specs are pretty similar.

So let's assume we can do the cruise.
If we cruise at 7000 km/h and mach 7 in the tropopause between 10 and 20 km height, the 6000 km cruise portion takes 51 minutes. That leaves roughly 5 min for takeoff and 5 min for landing. If we cruise at mach 8, 7.5 minutes for both.

First the boost problem. Bomarc was boosted to Mach 2 and some altitude before the ramjets started operating.
The delta vee is about 600 m/s for acceleration and 400 m/s for gravity and drag losses, so 1 km/s in total. With an ISP of 250 s that means a mass fraction of 1.5. Assuming a 34 ton after-boost mass, there are 17 tons of boost propellants needed. With a bit above 2:1 mixture ratio that's 12 t of LOX and 5 t of kerosene. Assuming 1 g of real acceleration, it takes just 100 s to reach 1 km/s. That saves a lot of time for landing. :)
The thrust needed for a horizontal takeoff could be about 400 kN, a Merlin-1 could produce that.

Here's a simplified mass table, in tonnes (t = 1000 kg):
*Propellants:
-Boost:
LOX: 12
Kero: 5
-Cruise:
Kero:8

*Tanks:
1 t (Tankage ratio 20)

*Engines:
Ramjet: 0.3 t (T/W=20)
Merlin-1: 0.8 t (T/W=50)
--
Total propellant and propulsion stuff:
27 t
after-boost:
10 t

Add wings and aerosurfaces, landing gear, crew compartment... They can weigh in total of 24 t.
The resulting vehicle could be somewhat bigger than an F-15.

Offline meiza

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Re: The V prize
« Reply #36 on: 12/03/2007 03:13 pm »
Let's calculate some more. :)
Let's assume a vehicle fuselage diameter of 3 m and no propellants in the wings. The tanks are cylindrical.
13 t of kerosene takes roughly 16 cubic meters of space, meaning 2.2 m length, and the
12 t of LOX takes 11 m^3 and 1.6 m. The four elliptical tank ends add about 0.25 m each meaning 1 m.
Total tankage length is thus about 5 m.

Here is some reading of a Mach 3 cruise missile, the Navaho, it was two-stage (kero booster, ramjet cruise), total mass about 30 t, payload 4.5 t:
http://www.astronautix.com/lvs/navhog38.htm

Offline meiza

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RE: The V prize
« Reply #37 on: 12/03/2007 11:38 pm »
I seem to have caught a morbid curiosity for this. Playing with NASA's public JAVA ramjet simulation tools, it seems that the ramjet engine's inlet, chamber and nozzle would all have to be actively cooled to stand up to the extreme temperatures when operating at mach 6.5 or over. Probably a hydrocarbon engine couldn't be used because of that. Each part sees about 2000 K temps.

Also the fuel flow with Jet-A would be 17 t per hour while with hydrogen it'd be 6 t.
The drag is enormous and the thrust only slightly bigger than it, resultin in a small net thrust.

Offline simonbp

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RE: The V prize
« Reply #38 on: 12/04/2007 01:46 am »
Quote
meiza - 3/12/2007  4:38 PM

The drag is enormous and the thrust only slightly bigger than it, resultin in a small net thrust.

And that's why noone has ever built a hypersonic airliner, and probably never will...

Simon ;)

Offline jongoff

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Re: The V prize
« Reply #39 on: 12/04/2007 02:43 am »
Quote
meiza - 2/12/2007  12:54 PM

If your distance is 6000 km, you would have to glide over 3000 km at least.
Given the very favourably assumed altitude of 50 km from where you could start gliding, this gives a slope of 1:60.

AIUI, depending on velocity and ballistic coefficient, can't you start experiencing lifting effects at a much higher altitude than that?  Ie most orbital vehicles flying lifting or semi-lifting trajectories, don't they experience noticeable lift even above 100km?

~Jon


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