I did a post on this a few years back, but couldn’t find it to repost.

A commentor in response to one of Rand Simbergs’ articles brought up (again) the old orbital is 8 times the velocity of suborbital and therefore 64 times as hard because energy goes as the square of velocity. Where to begin arguing this again?

The argument was that suborbital is Mach three vs orbital being over Mach twenty-four. Mach three won’t get you to space. 900 meters per second (~Mach 3) vertical velocity will get you 90 seconds of climb at an average of 450 meters per second, or about 40.5 kilometers of altitude. That doesn’t include drag, gravity losses during acceleration or engine back pressure losses. Mach 4 gets you 72 kilometers if you are in vacuum the whole time. It would take nearly Mach 5 to reach the Von Karmin line from sea level if you were in vacuum the whole way. 1,430 meters per second is considerably more than the 900 meters per second implied by the comment.

That was a straight up and down in vacuum from sea level. The flight doesn’t start in vacuum. Back pressure losses on a rocket engine gives 5-20% less performance at sea level than in vacuum. That is a major Isp hit on performance to a vehicle with a finite propellant capacity and facing exponential weight gain for excess mass. That 5-20% more propellant for a given thrust must be lifted by even more propellant. That extra propellant requires a larger airframe and engine capacity. The larger engine and airframe requires more propellant and so on. A suborbital vehicle has just as much back pressure loss as an orbital vehicle .

The vehicle has drag while it is accelerating toward space. The drag costs more propellant equals more engine and airframe, equals even more propellant and so on. If too much acceleration is done too early drag goes up by several more factors which would cost more propellant etc… Another aspect of the drag is heating if too much time is spent at high mach during the climb in the atmosphere. Thermal protection can get up there fast with a poor design. A suborbital vehicle has just as much drag loss in the climb out as an orbital vehicle.

There are gravity losses during the climb out. A suborbital vehicle has just as much drag loss as an orbital vehicle.

Actual mass ratios for suborbital above the Von Karmin line tend to be in the 3 to 4 range. If Mach 3 in vacuum was the whole story, then mass ratios would be in the 1.3 to 1.5 range. Orbital mass ratios tend to be in the 10 to 20 range depending on propellant choices and engine efficiency. The difference in mass ratios is about 4 to 5 with similar propellants. That is undeniably a major difference and order of difficulty. Just not 64 times the difficulty, especially with staging.

Life support is clearly different for manned vehicles. Bottled air for 30 minutes is different than 30 days for one. Food, toilet facilities, and creature comforts are quite different as well. This particular aspect may well be 64 times as hard. I doubt it, but it is possible.

Acceleration couches, controls, and displays will be about the same. More propellant for the RCS with the same number of thrusters is not that much more difficult. Communications will be more complex if the mission requires, though not an order of magnitude, and certainly not 64 times as hard.

Unmanned vehicle payloads have even less need for the 64 times as expensive meme. The energy supply is about the only thing that is clearly in a different league, though solar panels are getting to be quite well known even there.

Look at the historical record for more data. Working backwards from Elons’ billion investment in orbit with the 64 times as hard, any suborbital company spending more than 15 million should have been providing reliable service. Count for yourself the ones that have spent over 15 million and still don’t have an operational vehicle.

#### johnhare

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It helps to compare the Redstone to the Atlas. Both launched the same capsule, but Redstone (being sub-orbital) had a mass of 66,000 lbs and 78,000 lbs thrust while Atlas was 260,000 lbs and 300,000 lbs of thrust (1st stage), and 67,000 lbs of thrust on 2nd stage.

Four to one ratio. Quite different from the sixty four to one claimed.

But the Mercury Redstone was sub-orbital on steroids, traveling at 2.3 km/sec instead of Spaceship One’s 0.98 km/sec, with a brutal 11 G re-entry.

“Four to one ratio. Quite different from the sixty four to one claimed.”

Four to one is good way to look at it. But in terms of cost 64 to 1 might also

be another way to roughly look at it. Or $10,000 per suborbital seat seems

possible, or more plausible than $640,000 per orbital seat.

But main difference of suborbital and orbital is there is higher potential of seats one could sell, say within couple decades or a century. Or more than 5000 seats suborbital seats per year is more possible sooner than 50 seats to orbit and beyond per year.

The other thing important is the effort of reducing the 1400 m/s of delta-v needed by

rocket power. Or the contention of the article is it requires more than 1400 m/s

of rocket power for suborbital. But I would say the mothership launch lowers amount needed. Or Whiteknight two is supposed to launch from 70,000 feet [21 km] so in terms of rocket power, you aren’t going up 100 km, instead from the launch one is going 79 km up.

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra7

Put in 1250 m/s and 90 degrees and get 79719.38 meters.

Or 85 degrees and get about 79000 plus 21000 is 100,000 meters.

Then one add in any velocity imparted by the mothership velocity and angle it.

Plus a more vacuum condition for rocket launch

launches the rocket.

But the height without these factor adds 150 m/s.

And all other factors could be far more than 150 m/s.

Planes going straight up are a bit of problem, but if one you want more distance of travel with suborbital, one does need the plane going at such a high angle.

So stall speed at 70,000 feet is around 500 mph [225 m/s]. So at 21 km and going at least 225 m/s and rocket gets 220 m/s of it.

So 220 + 1250 is 1470 m/s. Put in 58 degrees, so goes 21 + 79.29 km high.

Distance this goes is same distance as 1400 + 220 at 58 distance[from sea level]

So travels 240 km, would have more zero gee, has roughly same gee load on re-entry- or less as one going shallower angle- hit denser air in longer period of time.

so from ground at 1400 at 90 degree the distance 2.4 meter. 85 is 34.7 km.

So one only adding about 200 km [124 miles] distance, but incremental change, not requiring much change in spacecraft.

Then if add say 100 m/s. So 1720 m/s reduce to 55 degree again from ground

the distance is 287.5 km. If mothership can go 225 mph faster or more rocket power.

Or mothership goes even higher than 70,000 ft [and it would need more speed- not to stall]

George,

The 0.98 km/sec would be at 52 km altitude in a vertical climb to reach space. There’s a lot of drag and gravity losses behind that number.

gbaikie,

$640,000.00 per orbital seat would be about$3,000.00 per pound. Somewhat above that which is current, and feasible as soon as human spaceflight becomes common. $10,000.00 for a suborbital seat is less than the current rates for high performance jet rides.

A couple of decades or a century is way too far out for realistic projection on seat sales to either destination.

The 1,400 meters per second is plus drag , back pressure, and gravity losses. A mothership gives just as much assistance to orbital as to suborbital vehicles.

–gbaikie,

$640,000.00 per orbital seat would be about$3,000.00 per pound. Somewhat above that which is current, and feasible as soon as human spaceflight becomes common. $10,000.00 for a suborbital seat is less than the current rates for high performance jet rides.–

High performance jets have one seat. XCOR at current prices can afford one seat, but not forever.

So cost is plane [even if it sits] and the pilot, more passenger per day lower costs.

Or jet flights at $25,000 per seat, may be a thing of the past. Though one could pay more for donkey ride than taxi.

Surely you can just use the first stage of any proper launcher to serve as your measure of sub-orbital vs orbital? They usually only have a few hundred km down-range and are just to get the second stage above the atmosphere for long enough to burn efficiently. That way you are comparing apples with apples, the same vehicle with it’s own components.

For example, F9’s first stage mass:payload ratio is about 4.5:1 (treating the second stage and payload as “payload” for the purposes of suborbital. Ie, 1st_stage + 2nd_stage + payload / 2nd_stage + payload.) The whole rocket has a mass:payload ratio of about 40:1. (1st + 2nd + payload / payload.) Suggesting that orbit is nearly 9 times harder than suborbital.

Paul,

Similar to my thoughts from a different direction. My complaint is with those claiming an exorbitant difference in difficulty based on a single figure of merit, and it flawed in the reasoning.

— john hare says:

October 10, 2014 at 2:59 am

George,

The 0.98 km/sec would be at 52 km altitude in a vertical climb to reach space. Thereâ€™s a lot of drag and gravity losses behind that number.–

I think George is referring to re-entry velocity. Or the max velocity attained according to wiki, was “8,262 km/h” [2296 m/s] for Mercury-Redstone 3 and

for Spaceship One, the max velocity attained was “Mach 3.09 (2,170 mph, 3,518 km/h)” [977.22 m/s].

So since went up at about 2300 m/s the Redstone would come down at about 2300 m/s. Whereas Spaceship One would come down [roughly] at about 977 m/s.

And since capsule was coming down faster it had higher Gee loads of “brutal 11 G re-entry”. Whereas Spaceship One peaked at about 8 G.

I would suppose the mercury capsule didn’t have more Gee loads, because it could be flown during en-entry and I would guess the trajectory was at around 45 degree angle- and/or capsule could be steered to fly at 45 or greater angle.

Whereas Spaceship One went roughly straight up and came straight down.

Though Spaceship One probably had greater cross section per it’s mass.

So with Spaceship One and Mercury-Redstone 3 the stated highest velocities [977.22 m/s and 2296 m/s] neither are the delta-v of the rockets, but rather the resulting velocities from the rocket.

To determine what gravity losses are involved one needs the flight profile before reaching such velocities.

With SpaceShipOne you can’t sensibly count gravity loss or air drag of the mothership [White Knight].

So if start, as one should, from the launch from mothership, one has “steering loss” to make the rocket go in right direction.

Or rocket is fired for about 10 seconds to do this [don’t know whether or how much of the time is full power in the “about 10 seconds”].

In terms of Mercury-Redstone Launch Vehicle, it looks like it would have a lot gravity losses: it’s weighed “30,000 kg (66,000 lb)” and had thrust of “350 kN (78,000 lbf)”

So it’s not jumping off the launch pad.

Whereas SpaceShipOne weighed “7,920 lb (3,600 kg) with thrust of “1 Ã— N2O/HTPB SpaceDev Hybrid rocket, 7,500 kgf ” . So more than twice the thrust of it’s mass.

So I would guess the delta-v of Mercury-Redstone was about 4 km/sec to reach it’s final velocity after “143.5 seconds” of burn time to reach 2.3 km/sec of velocity- and with the loss being mostly gravity losses.

Whereas with SpaceShipOne very fast acceleration and would have much lower gravity loss.

“If too much acceleration is done too early drag goes up by several more factors which would cost more propellant etcâ€¦”

Two things I will try focus on in my post.

In regard to suborbital trajectory [and using a rocket] I don’t think you have problem with too much acceleration in terms air drag [cost more propellent] – though not talking about structural considerations.

Second if “something” say launch assist or 1 stage adds about 200 m/s, and next stage doesn’t have as much initial acceleration you will not have much air drag- for suborbital or orbital trajectories.

Or either/ both, you will reduce amount of gravity loss by higher than the amount you lose from air drag.

This is my basic premise, due to my experience with my pipelauncher idea- that accelerates rockets by about 100 m/s.

I found instead that such addition of velocity **reduces** air drag on existing rockets.

To restate, If launch something straight up at about 100 m/s, which goes suborbital, it reduce gravity loss of any rocket by about 30%, and should reduce air drag on any rocket [though perhaps not sounding rockets or very fast accelerating rockets].

So pretty certain if add 100 m/s that this is the case and I would guess it works for +200 m/s or higher.

If look at SpaceshipOne’s acceleration which seems to me as fast acceleration for any suborbital rocket. Or roughly as you said:

“900 meters per second (~Mach 3) vertical velocity will get you 90 seconds of climb at an average of 450 meters per second”

SpaceshipOne’s burn rate according to wiki is “87 seconds”

It’s acceleration starting 20 to 21 m/s/s:

Thrust: 7,500 kgf and gross mass of 3,600 kg. [Empty weight is 1,200 kg]

And after 800 kg of fuel used: 26 m/s/s.

So if going up at 12 m/s/s for 40 seconds it reaches 9600 meter and traveling 480 m/s

That being over mach 1, at airline elevation with some drag, but it’s for seconds rather than minutes- a main concern is dynamic load rather than loss of delta-v from air resistance.

And next 10 seconds say it’s 14 m/s/s- that add 700 meter elevation and 140 m/s

And 10 second at 480 m/s adds 4800 meters. But let’s one has a fair amount of air drag and loss all of the 140 m/s added, one still has the 4800 meter added, so it’s 14400 meters high- or elevation one cruise at supersonic [fly for minutes to hours-

so seconds should not have much drag at that elevation.

Of course SpaceshipOne was designed to fly above 50,000, and it would very low air drag lost [a few meters per sec], but my point was one could have rocket with such high acceleration- get some air drag, but it would not have as much gravity loss-

so a net gain.

Now, if rocket accelerate for 40 seconds at 12 m/s/s how much gravity loss is occurring in those 40 second. It’s not 9.8 m/s/s for 40 seconds- that’s gravity, not gravity loss.

What does not have gravity loss is something fired from a cannon.

Shell goes up at 900 m/s and falls down at 900 m/s- no gravity loss.

If went up at 900 m/s and came down at 700 m/s then that would be 200 m/s of gravity loss. {though with cannon it would have to be air drag- cannon with instant acceleration don’t have gravity loss- rockets do.

If rocket is going straight up at 12 m/s/s it’s losing 9.8 m/s from gravity. So 40 seconds at 12 m/s/s is 480 m/s going vertical and reaching 9600 meter elevation

For the rocket’s delta-v: 12 + 9.8 m/s/s:

21.8 m/s/s. And for 40 seconds that is 872 m/s of delta-v

So take a cannon with muzzle velocity of 872 m/s and shoot it straight up. It will go

38,884 meter high and time of flight is 178.16 seconds, half that time for to get

to 38,884 meters.

But we want to know how fast it is going when cannon shell reaches 9600 meter.

It’s loses 9.8 m/s per second. So loses 9.8 m/s when travels first second, does straight

to distance of 862.2 meters, and then 852.4, and so on.

In 12 seconds it reaches 9699.6 meters, and the cannon shell going 754.4 m/s.

So rocket when reaches 9600 meter at velocity of 470 m/s at 12 m/s/s of acceleration and has used 872 m/s of delta-v.

Compare shell to rocket has about 754.4 – 480 which is about 274.4 m/s

274.4 m/s is the gravity loss from ground to 9600 meter elevation.

So that is rocket with fairly fast acceleration that when it used up 872 m/s of it’s delta-v, had lost 284.4 m/s from gravity, and as it uses more rocket fuel attaining higher velocity it will have some more gravity losses, but not very much.

Now compare to same rocket which is first boosted by adding 100 m/s.

If cannon gets 100 m/s to it, it does not have any reduction

in gravity loss- cannons don’t have gravity loss. But if have rocket which certain delta-v, as above where rocket had used 872 m/s to get to 480 m/s and 9600 meter, if add 100 m/s to rocket one must add 100 m/s to the cannon.

In order answer how much gravity loss is actually not lost.

Though if one is just concerned about the rocket, you could invent a term, called the

effective gravity loss [or something]. So we going start by to be interested in how

it just affects rocket performance. Maybe get other part later.

So, add 100 m/s to a rocket by assist launch of some kind.

And rocket in comparison flew for 40 second, the 100 m/s added will add

100 m/s in terms distance it goes for this time of 40 seconds. Times 100

by 40 seconds and add a 4000 km height to rocket, plus rocket will still be

going 100 m/s faster at this higher elevation. So instead of 9600 meter

one is at 13600 meters [44,619′] elevation, and be going 580 m/s rather

than 480 m/s.

A point of all this has to do with air drag. So if boost rocket by +100 m/s

how fast would be going when at the 9600 meter elevation?

If reduce the time from 40 to 32 second.

12 m/s/s in 32 seconds is 384 m/s and distance of 6144 meter.

100 m/s for 32 seconds is added distance of 3200 meters. So

484 m/s at 9344 meter.

Then add one second and it’s 496 m/s and 9834 meters.

And 32 1/2 seconds is 402 m/s and 9587.5 m/s.

So at 32 1/2 second point one is going 22 m/s faster and lower elevation- has more air drag as compare to 380 m/s at 9600 meters.

Not much difference and real rockets don’t have constant acceleration

they start out slower and increase their acceleration as they loss mass- and

that factor would swing it the other direction.

One could say that the gravity lost saving is 7 1/2 seconds of addition rocket

burn at higher elevation and better rocket engine performance [and less gravity

during that 7 1/2 of burn]. Or 7.5 times 21.8 m/s/s [163.5 m/s- and 613 meters higher] and one count one going 22 m/s faster. Compared to not boosted and having

274.4 m/s gravity loss. Or 274.4 minus [22 + 165.5 m/s].

Or “effective” reducution reduction gravity loses much more than 50% in terms getting the rocket to 9600 meter elevation. But as said in terms real gravity loses it’s more like 30%.

Or real is because if one gives rocket 100 m/s one must give cannon +100 m/s which

one comparing it to.

Now just for fun how do it compare to falcon 9. Or what are gravity loss of falcon 9

by time it get to around 9600 meter. Then maybe get gravity loss above 9600 meter-

in terms of suborbital I would guess 80 to 90% of gravity losses are below 9600 meters.

And main advantage of getting from 32,000 feet to 50000 ft [or higher] is in having

a shorter distance to 100 km and allowing lower angle which give more lateral

direction- if want suborbital to go a 500 km distance.

Or if you want to beat the March 6, 1990, 64 minutes, SR-71 Blackbird across America

at 3,418 km/h [.9494 km/sec] record. Wiki:

http://en.wikipedia.org/wiki/Cross-America_flight_air_speed_record

Wiki: Merlin: Thrust (SL) 147,000 lbf (650 kN)

9 times 1,323,000 lbf

Gross weight 1,115,199 lbs

Burn Time 180 sec

~385,000kg

385,000 divided by 180 second is 2138.88 kg per second

848,779.7 lb divided by 180 is 4715.4 lb per second

http://en.wikipedia.org/wiki/Merlin_%28rocket_engine_family%29

And vac:Thrust (vac.) 161,000 lbf

So in 30 seconds: 141,463 lb fuel is used.

1,323,000 – 1,115,199 = 207,801 lbf

1,323,000 – 973736 = 339,264 lbf

2 to 3.4 m/s/s

I could not believe this would have such slow take off speed.

In fact I am going assume it’s not fully fueled. And will make easier assume it does not have the 30 second of fuel.

So this give burn time of 150 seconds and 3.4 m/s/s launch acceleration.

And look at weight after another 30 seconds operation:

973736 – 141,463 is 832,273 lb

1,323,000 – 832,273 = 490,727 lbf

5.77 m/s

Such acceleration would bad a suborbital launch- great if boosted +100 m/s as one reduce a lot of gravity loss.

So first 10 seconds, uses 47,154 lbs of rocket fuel

973736 – 47,154 lbs is 926582

1,323,000 – 926582 = 396418 lbf

4.19 m/s/s

So 4 m/s/s for 10 seconds: 40 m/s and 200 meter elevation

20 seconds: 90 m/s and 850 meters

30 secs: 145 m/s and 2500 meters.

And delta-v used: 30 second of gravity: 294 And the 145 m/s.

And gravity loss as guess being about 200 m/s.

Or cannon at 439 m/s takes about 6 seconds to reach 2500 meters-

So more like 230 m/s gravity loss. And by time reaches orbit it have at least 1.5 km/sec of gravity loss. And again as rough guess, +100 m/s assist launch would half [or more] this gravity loss.

So it seems to me that for suborbital to work, one must have something like an assist launch- motherships like Virgin Galactic, or something else.

Something else could be a powerful but not with much rocket fuel mass as first stage which is reusable or something like cheap solid expendable.

Or step track mag lev or rocket boosted sled- need a mountain side.

Or my pipelauncher idea- which think a small one for suborbital could cost about a million or 2. And has cheap fuel cost and reuse.

Or if want to launch from deep water- just pipelauncher [a small one] could cost maybe about 1/5th million.

for water operation not including all infrastructure one might need- though a barge and crane could be enough.

But recent this post topic has got me thinking about having pipelauncher operate on the land.

So major cost of that would be digging a very big and deep hole and filling it with water. And possible cost of water would a significant operation and set up cost. Though the hole could a water well- even an artesian well.

gbaikie,

Ignoring drag because the vehicle only spends a few seconds there is akin to ignoring a foot of armor plate because a bullet crosses a foot in 1/3,000 of a second.

I have no idea how the rest of your extensive comment applies to the discussion. The work you have obviously put in is betrayed by the length and the diversity.

–Ignoring drag because the vehicle only spends a few seconds there is akin to ignoring a foot of armor plate because a bullet crosses a foot in 1/3,000 of a second. —

I am not ignoring air drag, rather I am saying that in terms to delta-v loses for a suborbital vehicle it’s not as significant as gravity loss.

I am assuming one is using a rocket. And I am assuming your trajectory is is near 90 degree vertical.

But if launching from mothership which flies to +50,000 feet and rocket payload trajectory is near vertical, then one ignore air drag for the upward leg of the trajectory.

Or let’s take this quote:

” One significant thing to realize is that higher thrust, and thus vehicular acceleration, results in a shorter flight time. Therefore, to minimize gravity losses, a higher acceleration is desired.

However, higher acceleration in an atmosphere can increase aerodynamic losses. So, an optimization between gravity losses and aerodynamic losses must be made for maximum overall delta V.” From:

http://orbitalaspirations.blogspot.com/2011/10/rocket-equation-and-small-rockets.html

So in regard to suborbital hops to 100 km and down, the “However, higher acceleration in an atmosphere can increase aerodynamic losses. …”

Is not applicable. Not regard to rocket which will carry crew. Or one is not balancing acceleration against gravity loss, one should trying to get most amount of acceleration

as is possible. And there will be air drag losses [and the structural considerations involved with this, though it should noted that re-entry will probably be a more of stress on airframe. Or put capsule blunt end up. it will experience load more coming down than one can make have going up].

Now, if one attempts to fly more horizontal rather than straight up, one can find much more air drag.

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