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 =97 up to the edge of space and return to

Earth =97 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=92s business plan. If price were

not an issue, nearly two-thirds of the respondents would

want to go on a round-the-moon adventure."

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 =3D 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 =3D 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) =3D Ve*ln[Mi/(Mi-rt)]. Then we can integrate this formula for

velocity to get the distance traveled, S(t):

S(t) =3D 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 =3D 2500 s, about 42 minutes, r =3D 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) =3D 3600*2500 - (3600/1)

***(1000)***ln

(3500/1000) =3D 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 =3D 3600*ln(3500/1000) =3D 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=92s spaceplanes.

by Sam Dinkin

Monday, August 9, 2004

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.

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.

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