SSASTOhttps://en.wikipedia.org/wiki/Douglas_SASSTO

The S-II stage of the Saturn V.

5 J2 engines 1,000,000 lbs thrust
Take off Weight 1,060,000 lbs weight
Structure 80,560 lbs
Ve=9,235 mph.

This can carry 34,100 lbs into LEO. About the size of a Gemini Capsule!

Today, we could do a Dragon Capsule!

Total take off weight with payload: 1,094,100 lbs.

Now, an aerospike engine, has a higher thrust to weight than a bell nozzle. It also has altitude compensating features which you've described below.

https://www.youtube.com/watch?v=-0Y0FS8Z1Qk

So, if you take 7 J2 pumpsets, and outfit a toroidal aerospike engine around it at the base of the S-11, and equip the zero height aerospike engines with a heat shield, you should using modern materials, attain the same structural fraction as was achieved in the 1960s with the S-II whilst increasing thrust to 1,400,000 lbs.

With a 9,235 mph exhaust speed a thrust of 1,400,000 lbf requires 3,323.8 lbs per second of propellant flow.

Acceleration is 42.2 ft/sec/sec minus 32.2 ft/sec/sec is 10.0 ft/sec/sec.

If we accelerate straight up for 100 seconds a total of 332,380 lbs of propellant have been burned. At that point the vehicle masses 727,620 lbs. So, acceleration rises at constant thrust to 1,400,000 lbf / 727,620 lbs = 62.2 ft/sec/sec minust 30 ft/sec/sec net that's

a = 42.2*exp(0.00388 * t)
V = integral(42.2*exp(0.00388*t) -32.2 ) dt, t=0 to 100 = 1,935.68 ft/sec = 1,319.8 mph.
D = integral(10,876.3 * exp(0.00388*t) - 32.2*t - 10876.3) dt, t=0 to 100 = 80,156.1 ft = 15.18 miles

Of course, you could start tilting the rocket, and calculate the cosine of the angle as vertical, and the sine of the angle as horizontal add them together to get total velocity, take the ratio to get the tangent and so forth..

av=cos(theta*t)*(42.2*exp(0.00388*t)-32.2)
ah=sin(theta*t)*(42.2*exp(0.00388*t))

at=sqrt(av^2+ah^2)
V=integral(sqrt(av^2+ah^2))
D=integral(integral(sqrt(av^2+ah^2)))

At $1,000 per pound, construction cost, the entire system would cost $85 million for the booster $35 million for the payload - $120 million total.


Reused 1200 times - the cost is $100,000 per flight. Propellant is $500,000 in quantity and maintenace $82,000 - between flights. That's $20 per pound.

http://www.spacefuture.com/archive/h..._systems.shtml


* * * *

On Tuesday, October 31, 2017 at 7:55:12 PM UTC+13, Robert Clark wrote:
"William Mook" wrote in message
...
You can buy them and do anything you can get a license to do. So, have at
it!
With a 3.2 km/sec exhaust speed and the requirement to boost through a 9..2
km/sec delta vee to attain a 7.91 km/sec orbital speed (with 1.29 km/sec
lost due to air drag and gravity losses) we have a propellant fraction of;
u = 1 - 1 / exp(9.2/3.2) = 0.943583860496223 ~ 94.36%
So, with a 3.5% structure fraction you could place 2.14% into LEO.
With a TSTO-RLV and the same structure fraction, dividing the delta vee by
2 to make each stage 4.6 km/sec we have;
u = 1 - 1 / exp(4.6/3.2) = 0.762479180904542 ~ 76.25%
So with a 3.5% structure fraction you could push 20.25% of each stage
through 4.6 km/sec.
So, here you have 0.202520819095458 squared which is 0.0410146821670953 ~
4.1%
Nearly double the take off weight into orbit.
Let's do three stages! 9.2 km/sec / 3 = 3.067 so,
u = 1 - 1 / exp(3.067/3.2) = 0.616468427123689 ~ 61.65%
So with a 3.5% structure fraction you have 0.348531572876311 ~ 34.85%
payload on each stage.
0.348531572876311 cubed is 4.23%
A slight, but measureable improvement.
So, you can see there is a significant benefit to two stages over one.
Now, if your structure fraction is higher, the benefit of staging is
higher. If we go from 3.5% to 5.0% structure fraction, we have

1 stage to orbit -0.64% - 155.85 t per t on orbit
2 stage to orbit - 3.51% - 28.44 t per t on orbit
3 stage to orbit - 3.71% - 26.96 t per t on orbit


Thanks for that calculation. It is correct, for the most part. There is the
fact that structure fraction only refers to the rocket stage itself without
payload. But when you calculate the fraction that reaches orbit, that's of
the entire mass including payload. So it's not quite accurate to subtract
off the structure fraction from this. But since the payload is a small
percentage of the entire stage mass it's a small discrepancy.

However, a key consideration that should be taken into account is that to
optimize the payload for a SSTO you really should use altitude compensation.
Your structure fraction for the stage of 3.5% is very good, but the exhaust
speed of 3.2 km/sec isn't very good for a vehicle you want to be SSTO.
Altitude compensation allows you to maximize your vacuum Isp while
optimizing your sea level thrust at launch as well.

Since we're discussing in the context of the Raptor engine I'll use
estimates for methane engines. I'll use a rocket engine analysis program to
estimate the possible vacuum Isp with methane fuel:

http://www.propulsion-analysis.com/index.htm

The specs of the Raptor in its latest incarnation are given he

https://www.freelists.org/archives/a...Xl97QZZkJ3.jpg

If you use the cited combustion chamber pressure of 250 bar of the Raptor,
but give it an expansion area ratio of 300, possible with altitude
compensation, then the vacuum Isp can be in the range of 390 s according to
the rocket engine analysis program.

In contrast, the sea level Raptors to be used on the BFR will have only a
vacuum Isp of 356 s, and even the vacuum optimized Raptors to be used only
have a vacuum Isp of 375 s. By using altitude compensation you don't have to
make these trades of how many sea level vs. vacuum engines to use. All the
engines will have the optimal performance both at sea level and at vacuum
with altitude compensation.

So let's redo your calculation assuming the good structure fraction of 3.5%
but using altitude compensation to improve the Isp to 390 s, exhaust speed
of 3,824 m/s.

Then the proportion of the rocket, dry mass plus payload, that reaches orbit
is: 1/exp(9200/3,824) = .09019, then subtracting off the .035 for structure
fraction, the payload fraction it would be .09019 - .035 = .05519, about
5.5%, significantly better than the 2.14% you get with only a 3.2 km/s
exhaust speed. Even more notable is that the payload fraction of the SSTO
with altitude compensation is even better than that of the TSTO without it.