I saw that this weeks Space Access '09 conference, http://www.space-access.org /,
will have several presentations by companies working on suborbital
flights for tourism.
According to this article, Virgin Atlantic is planning on marketing
just suborbital flights at $200,000 and it reports a survey said
orbital flights might be commercially viable at $500,000:

Space tourism survey targets cost factor. Online results hint at future price points for suborbital and orbital flights. By Leonard David Senior space writer updated 4:53 p.m. ET, Tues., Oct. 3, 2006 "Pricey seats. "So far, orbital space tourism has been the propelled province of well-heeled millionaires. Even for projected suborbital jaunts — up to the edge of space and return to Earth — the price tag for a Virgin Galactic spaceliner seat slaps your purse or wallet for roughly $200,000. Several key results of the space tourism survey point out: The prices of current space treks into suborbital and orbital are generally too high at present, with only 7 percent registering for a suborbital flight and 4 percent for an orbital adventure at current price levels. Suborbital flights would really take off at $25,000, and orbital flights at $500,000, if such price levels were compatible with an operator’s business plan. If price were not an issue, nearly two-thirds of the respondents would want to go on a round-the-moon adventure." http://www.msnbc.msn.com/id/15120091 /

I want to argue here that it would be feasible to provide service also for a much larger market: suborbital, hypersonic passenger flights for transcontinental and intercontinental transportation. A round trip cross-Atlantic ticket on the Mach 2 Concorde cost around $10,000. I don't think it's out of the question that a substantial number of business executives and wealthy vacationers would be willing to pay $100,000 to make a cross-Atlantic or cross-U.S. trip that took less than an hour, especially when it included making a short stint to space in the process. Likewise I think there would be a substantial market at $100,000 per ticket for a trip to Asia that only took 2 or 3 hours, compared to a full day as it does now.

You can make a calculation for how much fuel you would need for a rocket flying horizontally to reach a certain distance by using the rocket equation for velocity:

Vf -Vi = Ve*ln(Mi/Mf), where Vf, Mf are the final velocity and final mass, and Vi, Mi are the initial velocity and initial mass, and Ve is the exhaust velocity. The formula still works for intermediate points in the trip where you burned only a portion of the fuel, where Vf and Mf are the values at these intermediate times. Let's say you're burning propellant at a rate r kgs/sec. Then the mass of the vehicle at time t will be Mf = Mi-rt. I'll say the initial velocity Vi is zero, and let the velocity at time t be V(t). Then the formula becomes:

V(t) = Ve*ln[Mi/(Mi-rt)]. Then we can integrate this formula for velocity to get the distance traveled, S(t):

S(t) = Ve*t - (Ve/r)

This formula is for the case of constant thrust, where the acceleration will gradually increase since the mass is decreasing as the fuel is used up. It might be more comfortable for the passengers if instead we used a constant acceleration flight. This would be accomplished by making the fuel flow rate, and therefore thrust, decrease as the weight decreases. The formulas for this case can be constructed in an analogous fashion to those of the classic rocket equation. I haven't calculated it but my guess is the total fuel usage would be the same as for using the fuel at a constant rate. In any case, I will assume that just as for SpaceShipOne it will have aerodynamic shape to allow lift so that most of this propulsion can go towards providing horizontal thrust. I didn't include the drag in this first order calculation of the constant fuel rate case, but it can be added in a more detail examination. You can reduce the drag by having the craft undergo the hypersonic flight at high altitude. You can save fuel to reach this altitude by using a carrier craft such as the White Knight for SpaceShipOne. Note that you don't have to use the fuel on the carrier craft or suborbital vehicle to get to a height of say 100 km, but only to get to high enough altitude to reduce the drag and heating on the vehicle at the hypersonic velocities. XCOR is planning on using kerosene and LOX for their engines so I'll use this type of engine for getting the Ve number. Kerosene/LOX engines can have Isp of 360 s at high altitude, which I am assuming will be the only time the rocket will be used. So Ve will be in the range of 3600 m/s at high altitude. First let's say you want to go across the continental U.S., 4500 km. For a first generation transport vehicle let's say it's comparable in size to SpaceShipOne about 1,000 kg empty and 3,000 kg fully loaded with fuel to carry one pilot and two passengers. Let's put in some numbers in order to calculate the distance, S(t): say t = 2500 s, about 42 minutes, r = 1 kg/s, and Mi consists of a 1000 kg vehicle with passengers and 2500 kg fuel, for a total of 3500 kg. Then we calculate: S(t) = 3600*2500 - (3600/1)

X-15 and today’s spaceplanes. by Sam Dinkin Monday, August 9, 2004 http://www.thespacereview.com/article/204/2

Still carbon-carbon composites are used for the leading edges of the wings for the Space Shuttle which have to withstand the highest temperatures of re-entry even at Mach 25, so presumably would also work at Mach 15. These carbon-carbon composites became infamous though for how they fractured under impact by foam in the Columbia accident. It turned out they are even more brittle than fiberglass. This is a bit puzzling because the type of carbon composites used extensively for example in modern race cars is actually more fracture resistant than steel. This makes them an ideal material for race cars since they have greater strength than steel while being more fracture resistant and at a fraction of the weight. I can only assume that at the time the shuttle was being designed, these highly fracture resistant carbon composites were not available. Then the recommendation for the thermal protection is the carbon-composites of this highly fracture resistant type. For the vehicle to be useful as a transport craft it will have to be able to take-off and land at least at international airports. Airport safety managers might not be too enthusiastic about rocket takeoff at their airports, and certainly not enthusiastic towards deadstick landings. At least for the takeoffs this uncertainly be could ameliorated by the jet engine carrier craft. For the landings I suggest these rocket craft also have their own small jet engines so that they can do powered landings. There are some lightweight jet engines that could work for our 1000 kg first generation craft. For instance there is the TRS-18-1 engine that can produce 326 pounds of thrust and only weighs 85 pounds:

Microturbo TRS-18-1 Engine Specifications. http://www.bd-micro.com/FLS5J.HTM#ENGINE

Two of these would probably be sufficient for landing our 1000 kg rocket plane assuming at subsonic speeds the craft had a lift/drag ratio typical for jets, which can be at 10 and above. A more high performance and more extensively tested jet engine to use might be the PW610F. This weighs 260 pounds and can produce 900 pounds of thrust:

Pratt & Whitney Canada PW600. http://en.wikipedia.org/wiki/Pratt_%26_Whitney_Canada_PW600

One of these would probably sufficient for our purposes. For this more high performance engine we might even be able to use it for takeoff to reach high altitude for the rocket plane, dispensing with the need for the carrier craft. At this early stage, we would have separate jet engines and rocket engines. The jet intakes would be closed off when the rocket is operating and opened to be used only during low speed, subsonic flight. However, we can imagine with further development we would get a type of hybrid engine, as for example envisioned for the Skylon craft, where the jet and rocket engine are combined into one.

Bob Clark

Space tourism survey targets cost factor. Online results hint at future price points for suborbital and orbital flights. By Leonard David Senior space writer updated 4:53 p.m. ET, Tues., Oct. 3, 2006 "Pricey seats. "So far, orbital space tourism has been the propelled province of well-heeled millionaires. Even for projected suborbital jaunts — up to the edge of space and return to Earth — the price tag for a Virgin Galactic spaceliner seat slaps your purse or wallet for roughly $200,000. Several key results of the space tourism survey point out: The prices of current space treks into suborbital and orbital are generally too high at present, with only 7 percent registering for a suborbital flight and 4 percent for an orbital adventure at current price levels. Suborbital flights would really take off at $25,000, and orbital flights at $500,000, if such price levels were compatible with an operator’s business plan. If price were not an issue, nearly two-thirds of the respondents would want to go on a round-the-moon adventure." http://www.msnbc.msn.com/id/15120091 /

I want to argue here that it would be feasible to provide service also for a much larger market: suborbital, hypersonic passenger flights for transcontinental and intercontinental transportation. A round trip cross-Atlantic ticket on the Mach 2 Concorde cost around $10,000. I don't think it's out of the question that a substantial number of business executives and wealthy vacationers would be willing to pay $100,000 to make a cross-Atlantic or cross-U.S. trip that took less than an hour, especially when it included making a short stint to space in the process. Likewise I think there would be a substantial market at $100,000 per ticket for a trip to Asia that only took 2 or 3 hours, compared to a full day as it does now.

You can make a calculation for how much fuel you would need for a rocket flying horizontally to reach a certain distance by using the rocket equation for velocity:

Vf -Vi = Ve*ln(Mi/Mf), where Vf, Mf are the final velocity and final mass, and Vi, Mi are the initial velocity and initial mass, and Ve is the exhaust velocity. The formula still works for intermediate points in the trip where you burned only a portion of the fuel, where Vf and Mf are the values at these intermediate times. Let's say you're burning propellant at a rate r kgs/sec. Then the mass of the vehicle at time t will be Mf = Mi-rt. I'll say the initial velocity Vi is zero, and let the velocity at time t be V(t). Then the formula becomes:

V(t) = Ve*ln[Mi/(Mi-rt)]. Then we can integrate this formula for velocity to get the distance traveled, S(t):

S(t) = Ve*t - (Ve/r)

***(Mi-rt)***ln[Mi/(Mi-rt)]This formula is for the case of constant thrust, where the acceleration will gradually increase since the mass is decreasing as the fuel is used up. It might be more comfortable for the passengers if instead we used a constant acceleration flight. This would be accomplished by making the fuel flow rate, and therefore thrust, decrease as the weight decreases. The formulas for this case can be constructed in an analogous fashion to those of the classic rocket equation. I haven't calculated it but my guess is the total fuel usage would be the same as for using the fuel at a constant rate. In any case, I will assume that just as for SpaceShipOne it will have aerodynamic shape to allow lift so that most of this propulsion can go towards providing horizontal thrust. I didn't include the drag in this first order calculation of the constant fuel rate case, but it can be added in a more detail examination. You can reduce the drag by having the craft undergo the hypersonic flight at high altitude. You can save fuel to reach this altitude by using a carrier craft such as the White Knight for SpaceShipOne. Note that you don't have to use the fuel on the carrier craft or suborbital vehicle to get to a height of say 100 km, but only to get to high enough altitude to reduce the drag and heating on the vehicle at the hypersonic velocities. XCOR is planning on using kerosene and LOX for their engines so I'll use this type of engine for getting the Ve number. Kerosene/LOX engines can have Isp of 360 s at high altitude, which I am assuming will be the only time the rocket will be used. So Ve will be in the range of 3600 m/s at high altitude. First let's say you want to go across the continental U.S., 4500 km. For a first generation transport vehicle let's say it's comparable in size to SpaceShipOne about 1,000 kg empty and 3,000 kg fully loaded with fuel to carry one pilot and two passengers. Let's put in some numbers in order to calculate the distance, S(t): say t = 2500 s, about 42 minutes, r = 1 kg/s, and Mi consists of a 1000 kg vehicle with passengers and 2500 kg fuel, for a total of 3500 kg. Then we calculate: S(t) = 3600*2500 - (3600/1)

***(1000)***ln (3500/1000) = 4,490,000 meters, or 4,490 km. The time of 42 minutes compares to about 6 hours for a normal passenger jet to travel this distance. The maximum speed would be Vf = 3600*ln(3500/1000) = 4500 m/s, or Mach 15, quite a high speed. The X-15 was able to reach Mach 6.7 and was planned on being able to reach Mach 8. It had an Inconel skin with a titanium frame to resist the heat loads at these high Mach numbers. Still for Mach 15 you might need materials even more heat resistant. In this article Burt Rutan says SpaceShipOne's carbon composite structure would not be sufficient for even the Mach 6.7 speeds of the X-15:X-15 and today’s spaceplanes. by Sam Dinkin Monday, August 9, 2004 http://www.thespacereview.com/article/204/2

Still carbon-carbon composites are used for the leading edges of the wings for the Space Shuttle which have to withstand the highest temperatures of re-entry even at Mach 25, so presumably would also work at Mach 15. These carbon-carbon composites became infamous though for how they fractured under impact by foam in the Columbia accident. It turned out they are even more brittle than fiberglass. This is a bit puzzling because the type of carbon composites used extensively for example in modern race cars is actually more fracture resistant than steel. This makes them an ideal material for race cars since they have greater strength than steel while being more fracture resistant and at a fraction of the weight. I can only assume that at the time the shuttle was being designed, these highly fracture resistant carbon composites were not available. Then the recommendation for the thermal protection is the carbon-composites of this highly fracture resistant type. For the vehicle to be useful as a transport craft it will have to be able to take-off and land at least at international airports. Airport safety managers might not be too enthusiastic about rocket takeoff at their airports, and certainly not enthusiastic towards deadstick landings. At least for the takeoffs this uncertainly be could ameliorated by the jet engine carrier craft. For the landings I suggest these rocket craft also have their own small jet engines so that they can do powered landings. There are some lightweight jet engines that could work for our 1000 kg first generation craft. For instance there is the TRS-18-1 engine that can produce 326 pounds of thrust and only weighs 85 pounds:

Microturbo TRS-18-1 Engine Specifications. http://www.bd-micro.com/FLS5J.HTM#ENGINE

Two of these would probably be sufficient for landing our 1000 kg rocket plane assuming at subsonic speeds the craft had a lift/drag ratio typical for jets, which can be at 10 and above. A more high performance and more extensively tested jet engine to use might be the PW610F. This weighs 260 pounds and can produce 900 pounds of thrust:

Pratt & Whitney Canada PW600. http://en.wikipedia.org/wiki/Pratt_%26_Whitney_Canada_PW600

One of these would probably sufficient for our purposes. For this more high performance engine we might even be able to use it for takeoff to reach high altitude for the rocket plane, dispensing with the need for the carrier craft. At this early stage, we would have separate jet engines and rocket engines. The jet intakes would be closed off when the rocket is operating and opened to be used only during low speed, subsonic flight. However, we can imagine with further development we would get a type of hybrid engine, as for example envisioned for the Skylon craft, where the jet and rocket engine are combined into one.

Bob Clark