# Mach 3 aerodynamic drag

1. Oct 5, 2015

### Bob584

Hello everyone. Recently I have had a lingering need to (in a loose sense) conceptualize the aerodynamic resistance of an object traveling at high supersonic velocity. However it has been a long time and I am rusty on my physics. I am looking for a ballpark figure on the Newtons and Joules (1 hour of travel) required at velocity and do not have a specific physical aircraft design so I am neglecting skin friction, induced drag, wing properties etc...

So, cheating and using wiki....

https://en.wikipedia.org/wiki/Drag_(physics)

The power required to overcome the aerodynamic drag is given by:

the p value (100,000 feet = 0.0183 [p metric]) I got from this chart
https://user.engineering.uiowa.edu/~cfd/pdfs/tables/7-2B.pdf

For the theoretical values I set A (cross sectional area) to 7.0 square feet and the Coefficient of drag to 0.03. Velocity is 1020.86 m/s.

So plugging in the numbers I get..... 2,044,273.27 N?
This is where I get confused, its always been a unit issue with me. I assume that the number above is in Newtons but when I try to figure out the energy required to keep up 1020.86m/s for 1 hour (3,675,096 m) W=FD I get this huge number of 7.51 x 10^12 J? of energy.

This doesn't seem right and its probably something simple I am missing that is compounding but I cannot see it; the energy given in my conclusion feels much too high.

Any help is greatly appreciated, thank you for your time.

2. Oct 5, 2015

### SteamKing

Staff Emeritus
Since Pd is the power required to overcome aerodynamic drag, then its units will not be newtons, but watts (= N-m/s). The drag force, Fd, will have units of newtons.

Also, since ρ is in units of kg / m3, then A must be in units of m2 to produce the correct power calculation. v is in m/s.

3. Oct 5, 2015

Where did you come up with that arbitrary drag coefficient?

4. Oct 5, 2015

### Bob584

@SteamKing

Silly me. Thank you kindly for helping me and my muddle good sir!

I found out that the Phantom F4E had a ratio of 0.044, I then just picked 0.03 thinking that if SST travel were ever to become feasible the engineering would probably have to be close to that area to keep the energy costs a bit more manageable. In the end the number is, as you say, fictional.

http://www.dept.aoe.vt.edu/~mason/Mason_f/ConfigAeroSupersonicNotes.pdf
But the physics and math is far too advanced for me, hence the reason I wanted to keep the calculation simple and not try my hand at an actual theoretical design.

5. Oct 6, 2015

### SteamKing

Staff Emeritus
The Concorde SST used 4 Rolls-Royce Olympus 593 turbojets to power it to a Mach 2.0 cruising speed. At that speed, each engine reportedly was producing power equivalent to 36,000 HP, so with the Concorde using 4 engines, that's 144,000 HP total.

https://en.wikipedia.org/wiki/Rolls-Royce/Snecma_Olympus_593

The Olympus 593 plant is rated at 38,000 lbs of thrust.

The proposed Boeing SST which was cancelled in 1971 was a larger aircraft designed to fly at Mach 2.7. It was intended to use 4 GE4 turbojets, each rated at 63,200 lbs max. thrust w/afterburner.

https://en.wikipedia.org/wiki/Boeing_2707

You can see that barring some major breakthroughs in aerodynamics, future SSTs are unlikely to be developed, given the massive power requirements and attendant fuel consumption these aircraft require.

6. Oct 6, 2015

The thing is, there have been breakthroughs in aerodynamics. The problem with planes like the Concorde and earlier SST designs was not just that they required a lot of power while flying supersonic, but perhaps more importantly that they required even more power when flying subsonic trying to reach those speeds. Their designs were really only "efficient" when supersonic because the concepts behind efficient plane design are very different depending on which side of 1 the design Mach number happens to be.

Aerodynamics have had breakthroughs since then, as evidenced by the fact hat there are several business jet-class SSTs in the works.

7. Oct 6, 2015

### SteamKing

Staff Emeritus
There always seems to be some SST "in the works", and even the US kept researching large SST development for a while after the cancellation of the Boeing SST in 1971.

However, a bizjet SST is not the same beast as something like a Concorde, and none of these putative designs seems to have leapt from paper to prototype yet.

The power requirements for such a plane are daunting, but by no means are they the only problems which stand in the way of development or operation of such a plane should it be built. Supersonic flight corridors are still prohibited over most populated areas except for military aircraft, and the reported cost of some of these planned commercial aircraft is breathtaking.

8. Oct 6, 2015

### Bob584

Originally the Concorde had secured about 100 orders over 16 different airlines before the bans on SST travel over land came into effect. While not the sole reason for the Concorde's demise such an act did cripple its economic prospects, allowing the program to survive with 20 aircraft under heavy government subsidization. In the case of making possible a mach 3 aircraft, (business or commercial) tremendous obstacles would have to be overcome; the ban on overland SST travel and economic reasoning probably being the highest. Awhile ago I contacted Gulfstream with the question: "Does Gulfstream have any R&D prospects on supersonic flight?"

Of which their response was: "We have a modest R&D program dedicated to sonic-boom suppression. Until the ban on supersonic flight over land is lifted, we don't see a business case for a supersonic business jet."

Figuring out safety systems to counter emergency depressurization at 100,000 feet would also be a prime concern as at that altitude such an event would likely kill instead of incapacitate. Then there is the robust thermal resistant material engineering that would have to deal with the extreme skin friction, the sonic boom suppression as gulfstream has stated, and safeguards for stability control in the event of a malfunction. (The SR-71A 61-7952 was completely destroyed in flight due to an engine unstart)

Still in an age where heuristic growth on all fronts are nearly asymptotic, big goals such as this are not impossible, just extremely difficult to solve. I can eventually see such implementation resurfacing for over-ocean use, but it is likely that if hyperloops become successful then that method of travel will probably dominate landmasses.

Last edited: Oct 6, 2015
9. Oct 6, 2015

You guys might want to check out the company Aerion. They are serious enough that they have investment from/collaboration with Airbus ongoing. They are targeting a 2019 flight test. Of course it may yet falter, but they do have solutions (or partial solutions) to all the problems cited here so far, including at least a partial fix for the horrendously bad performance of supersonic aircraft at subsonic speeds and sonic boom mitigation.

We aerodynamicists know a lot more now than we did when the Concorde was designed.

10. Oct 6, 2015

### SteamKing

Staff Emeritus
I have. At an estimated $120 million a copy, the Aerion aircraft will have to perform in a radically serious way to justify its acquisition and operating expense. http://robbreport.com/aviation/aeri...s-its-120-million-as2-supersonic-business-jet And it's not aerodynamics which is holding back widespread supersonic travel so much as economics. When it was designed, the original Concorde might have been able to eke out a profit when oil was selling for$2 a barrel, but after oil quadrupled in price to \$8 a barrel after 1973, the only thing left for the Concorde to demonstrate was national pride, since all hope of any profit making went out the window, and the aircraft kept flying only because its operations were heavily subsidized by the British and French governments.

While Airbus may now be involved with the design of the Aerion, their continued involvement in the future is not guaranteed. Airbus has already extended itself on the A380 super jumbo program, and the bloom may be coming off that rose as the first round of those aircraft are coming up for renewal of their leases or are being shopped on the second-hand aircraft market. Airbus is struggling to find enough new customers to keep the production line open, reportedly.

http://www.bloomberg.com/news/artic...80-superjumbo-worth-airbus-is-set-to-find-out

11. Oct 6, 2015