Only if you fly at the same altitude. Notice the density term in that drag formula? By flying at a higher altitude, the lower density compensates for the higher airspeed, which results in the same drag force. A higher altitude flight results in higher true airspeed for the same
equivalent airspeed.
SO.............
You are stating something which is apparent and was already encountered by me in my analysis.
This was your post ...........
Actually, it could be much more efficient by flying hypersonically in the outer atmosphere. Basically, the faster you fly, the shorter amount of time you need to stay in the air for any given distance. This means less fuel consumption.
Your assertion was that because hypersonic missiles are flying fast,they need to stay in air for shorter amount of time and thus fuel consumed would be less.
Now what i proved was that for same altitude a missile travelling at steady hypersonic velocity in cruise mode ( no acceleration hence no force required in vacuum situation) would be acted upon by far greater drag force than a supersonic one hence the missile would have to burn more fuel to overcome that drag force.
The difference in densities did not came into play as both missiles were supposed to be travelling at same altitude.It was to disprove that faster travelling missile requires less amount of fuel.
The post also violates first law of thermodynamics.It is equivalent to saying that if i drive faster than my car would consume less amount of fuel for same distance.
This is the formulae of Air drag
Only if you fly at the same altitude. Notice the density term in that drag formula? By flying at a higher altitude, the lower density compensates for the higher airspeed, which results in the same drag force. A higher altitude flight results in higher true airspeed for the same
equivalent airspeed.
Probably you did not understand the meaning of the link you have provided......
A higher altitude does not result in higher truespeed.Truespeed is the speed that the body possesses.The difference if only in the term of equivalent speed.
Only if you fly at the same altitude. Notice the density term in that drag formula? By flying at a higher altitude, the lower density compensates for the higher airspeed, which results in the same drag force. A higher altitude flight results in higher true airspeed for the same
equivalent airspeed.
Let's make a simple calculation which would put this thing to rest.
Formulaes:
Earth Atmosphere Model - English Units
For troposphere
T = 59 - .00356 * h
p = 2116 * [(T + 459.7)/ 518.6]^5.256
r = p / [1718 * (T + 459.7)]
Now let's say a missile is cruising at an altitude of 100feet
T= 58.644[SUP]o[/SUP] F
p= 2110.5 lbs/ft[SUP]2[/SUP]
r= 0.00237 slugs/ft[SUP]3[/SUP] = 1.22 kg/m[SUP]3[/SUP]
For upper stratosphere
T = -205.05 + .00164 * h
p = 51.97 * [(T + 459.7)/ 389.98]^-11.388
r = p / [1718 * (T + 459.7)]
Let's say a missile is cruising at 83000 ft
T= -68.93 [SUP]o[/SUP]F
p= 50.786 lbs/ft[SUP]2[/SUP]
r= 0.00075648 slugs/ft[SUP]3[/SUP] = 0.38987 Kg/m[SUP]3[/SUP]
Now the formulae for drag has one power of density but square of velocity.
The ratio of density of air at ground level and upper stratosphere is Ground/Stratosphere = 31.32
Now let a supersonic cruise missile (Mach 1.2) is travelling at ground level while a hypersonic cruise missile is travelling through stratosphere (Mach 7)
Drag force on Supersonic/hypersonic = 31.32 X 1.2[SUP]2[/SUP] / 7[SUP]2[/SUP] = 0.92
ie a hypersonic missile cruising in upper stratosphere 1.08 times the drag faced by supersonic cruising at ground level and 34 times that faced by supersonic missile at same altitude.
In exact terms
C[SUB]D[/SUB] = 0.75 for a typical model rocket
Drag coefficient - Wikipedia, the free encyclopedia
Let the missile has diameter of 1 m
so area = 0.758 m[SUP]2[/SUP]
For hypersonic (Mach 8)
F[SUB]d[/SUB]= 651201.2 Newton = 66449.1 KgF = equivalent of 66.45 tonnes.
Now a missile weights only 2-3 tonnes in the beginning.So the drag force acting on a hypersonic missile is 33 times that of its weight.ie Drag is not the force which is negligible.
But we aren't firing in a vacuum and we're acting under the influence of gravity. The amount of energy required to accelerate to hypersonic speeds is miniscule compared to the amount of energy required to keep the missile from falling to earth during its flight.
I gave example of vacuum as an ideal system where drag force = zero hence only vertical component of force is present.In reality both vertical and horizontal force is present.
The amount of energy required to keep a Hypersonic missile in sky is 30 times less than that which is required to maintain it's speed.and since the vertical force depends on weight of a missile which is in range of 2-3 tonnes and most of which is propellent which is used during boost phase,Fuel required for hypersonic missile is much more than that required for supersonic.
And most of the fuel is consumed by a rocket/missile in accelerating to hypersonic speeds.
This is why scramjets aren't being used for aircraft. It just isn't practical. But it certainly would be quite feasible for a cruise missile to have a small first stage that accelerates it to supersonic speeds for the scramjet to start up.
The bigger problem is wether the decreased flight time due to increased speed will make up for the fall in fuel efficiency due to using a scramjet. Theoretically speaking, the two should cancel each other out. But in practice, it really depends. Certainly, the turbofan has been around a lot longer to be perfected, so the scramjet is at a disadvantage here.
The efficiency of scramjet engine is worse than both rocket and turbojet engines.
Similarly efficiency of turboJet engines is less than that of piston cylinder engine.
If efficiency have been sole criterion than anyone would opt for radial piston engines for aviation.
But it is not so because there is a maximum speed limit up to which a engine could function.
A scramjet could not be compared to a turbojet as a turbojet could not achieve hypersonic velocities.Here Scramjet has to be compared with rockets which even though have greater efficiency tends to be bulkier as they need oxidiser.
Scramjet are also impractical to be used for satellite launch as they could not obtain orbital velocity even though they go hypersonic.For missiles also their ceiling limit is lower than that of rockets as they are air breathing.