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Okay, I'm going to talk about what's special about hypersonic flight,
what's different to hypersonic flight when flight in any other flight regime and where do you
do hypersonic flight? Why would you - why would you travel so fast in the atmosphere,
where you get very hot and there's lots of friction around.
Well, hypersonic flight by implication you have to be in an atmosphere, out of space you go
very fast but you don't really call it hypersonic flight unless you're in the
in an atmosphere. In going very fast - there are a lot of aerodynamic effects like: lift, drag, heat transfer.
They can be useful to you and they can be a disadvantage.
We'll look first about where do you fly, what's sort of things do you do
when you fly. Depending on what your mission is that has a strong influence
on the shape and the design of the flight vehicle you use.
We can categorise certain commonly used flight paths.
The most well known is the re-entry corridor when you come back from outer space
and it's a good idea to stop before you hit the ground because you're travelling very fast.
The cruise corridor: that's when you want to travel at a constant speed and just
travel places fast. The cruise corridor actually hardly exists at the moment because
we don't know how to do it in a sustained manner. And acceleration corridor relates to
when you're trying to accelerate to go through the hypersonic flight regime and get into space.
Again it's not something we do particularly at the moment because
we don't have a propulsion systems to facilitate it. And then there's more likely
the common thing is : sub-orbital 'space hops' : where you want to shoot something up
very fast, get out of the atmosphere and then come back in again at a
some distant location and travel very fast as you do it.
What you might think of a hypersonic flight trajectory actually isn't.
The normal way of getting into space is not to fly hypersonically.
You need to go at speeds in space that are much faster than hypersonic but actually
you're trying to do that acceleration outside the atmosphere. So the space shuttle
for instance, although it will have a normal Mach number of 25 when it's at
space it's very hypersonic, it leaves the atmosphere by about Mach 3.
It goes straight up and out of the atmosphere as quickly as it can
because it's not a good place to be when you're travelling very fast in an atmosphere -
lots of drag, lots of heat transfer, you're likely to burn up and self-destruct.
Well we've been using re-entry corridors for about 60 years since the first missiles went up
into space. The main function of re-entry corridor is just to lose
speed and in doing that if you want to survive, you've got to control
your drag, your deceleration. You can easily be destroyed just
through too many G-forces and also heat transfer; lots of energy around which can
burn you up if you're not careful. There are several categories of ballistic trajectory
the ones we're going to look at here are the so-called ballistic trajectories
where we have only drag and no lift. Most flight trajectories will
actually make use of lift to a certain amount - like the Apollo coming in at a lifting trajectory.
But ballistic trajectories are very good because you can get analytical solutions for them
and we often use a ballistic trajectory as a starting point for a design study
because you can get quite close to what a flight path might really be.
And you get analytical solutions which is a good thing to have at the start of the design
process. You know roughly where you're flying - which is how high and I guess which
atmosphere - and how fast you're going and then you can have a stab at designing a
vehicle. So ballistic entry relates to using drag forces to slow yourself down.
The three basic categories within a ballistic trajectory : aerocapture is not
actually being done yet but we talk about it a lot and that relates to coming in from
outside of the Earth, and it was so-called hyperbolic trajectory outside of gravity's
influence and you have to slow down enough in the atmosphere
to get captured but not actually to land. Aerobraking may can be used to adjust the
capture orbit by ducking down in the atmosphere for a little while
and losing some velocity and then going out again.
You might wonder why would you do that. Well if you want to change your orbit
and you don't use braking, you have to fire up rockets and
rockets are heavy and they have to carry fuel. So it's a way of losing your speed
without having a propulsion system to do it. And most commonly used trajectory
of course is the total re-entry where you come in from outside and you stop and
you adjust things to get the right control of velocity along the way through the atmosphere.
Okay, what sort of vehicle will we like to build for re-entry?
You know traditional aerodynamicist like to make things that look nice and sleek and sort of sexy
and they turned out - you know they don't work very well for re-entry purposes because
the purpose isn't to generate lift and fly long distances with minimum amount of fuel,
it's to stop. So typically re-entry vehicles are characterised by surfaces aligned normally to the flow,
so the force that acts on them is pushing against your direction of motion.
So in any field of engineering,
a good idea as a starting point when you go into a new application is to look at
what people did before and see if it's going to work. If you don't do that,
you're likely to reinvent the wheel.
So when we first had the capability to go hypersonically in the '50s,
we looked at what's the traditional aerodynamic shape and it's
like you see on the left there - it's something long and slender looking. And they'd
analyze that, they tested it in wind tunnels, and it really didn't work very well.
You can imagine if you use that long skinny thing as a brake,
the main surfaces you have for braking are friction surfaces. It's like trying to slide
down a rope,
you rub all the skin off your hands through friction and that's not the way to go.
So the big breakthrough came in the 50s when they decided you don't make
long slender things, you make blunt bodies. And that's been the way we've
done it ever since, so it's self-evident what you do - it's blunt, it
pushes the air out of the way, it slows you down and the heat transfer is minimised.
Even if you look at something that's quite streamlined like the space shuttle,
on re-entry it flies more like a brake. It comes in at like 40 degrees to the
flight path and most of the surfaces are pointing forwards. Obviously it generates
some lift as well which we're not going to analyse in this course, but it's the blunt body
dissipating heat. You see the same vehicle later when it comes into land,
it flies in a very different mode. Here's an example of a flight vehicle coming through the atmosphere,
all the energy is being dissipated as radiation in the shock layer, you can see it glowing.
And when it lands and people come out, hopefully they survived, you can see it's
a very simple blunt body shape, it doesn't really look sophisticated
but actually technically it's a very advanced design. Getting people back from space
alive and safe, is not easy.
This is a classic design called the sphere-cone configuration,
shown here in a Titan entry capsule.
You want to make the thing as blunt as you can because that's the most efficient shape.
Because if you make it blunt, you introduce another problem - all your drag forces are
on the front because your mass has to be behind the front surface. It is effectively unstable as
if you try and balance something with all its weight beyond the point tof support.
You see those front surfaces are flared back a bit and
by flaring them back, you reduce their efficiency as the aerobrake
a little bit, but you're moving the centre of drag further downstream so it's
easier to handle the stability So that's the classic shape we use for re-entry
into the earth or other planets at high speeds as well.
Okay we'll look now at doing some simple sums as to
find out - if you're doing a re-entry where are you going to be at say
50 kilometres altitude, how fast would you be going? That sort of
fundamental equation you would use. So the first starting point is to use what we call
flat Earth trajectory where you ignore the curvature of the earth, (seems to work very
well in Queensland) and it gives you a very good starting point for analysis.
So this equation is very simple you have drag because there's no lift, it's
back into the direction you're flying. You've got a velocity vector and you've got gravity
pulling from one side. And the important parameters are how high are you,
what angle are you flying, and how fast are you going?
So we can write down some basic equations we have these
in more detail in the associated documents,
They're very simple - it's a dV/dt term which is your deceleration.There's a
dy/dt - that's how fast you're falling vertically through the sky
which is just a function of what angle you're flying at and how fast you're going - simple geometry.
Then of course you got to bring your mass into it, so the mass times deceleration
gives you the forces that relates to drag and gravity. Your angle will be changing as you -
as you fly through the sky, as you change your direction you have to rotate the velocity vector.
So transverse force is needed normal to your flight to keep rotating the velocity vector
and in fact we'll ignore this second term in a minute.
Okay typically if it's hypersonic flight,
it's a big number, your velocity is big and these terms all scale with V^2.
So V^2 is pretty close to infinity, so if your feature is small, you can see from the equations
that dθ/dy will be small as well, so why not as the starting point
ignore any changes in angle as you fly and pretend it's a straight line flight path.
It's - you know don't go and fly the stuff I'm going to teach you, you'll kill yourself,
but use it as a starting point to get your first design ready.
And when you have a spacecraft that might be close to being
usable then you go and do the sums properly through computational techniques.
But you need the simple approach first,
just to get started and that helps you to understand some of the physics that
is associated with the flight. Okay, a few pages of algebra which you can look up
in the support documents that enables you to extrapolate
or extract if you like - the time variable from the equations. You get
to the final form of the equation which can be integrated if you know the density,
its how your velocity changes with altitude as a function of density.
And there's other terms in there that relate to the aerodynamic characteristics
of your flight - drag coefficient area and mass, and of course your angle you're flying at.
We need to know density, well we do to know density to a certain extent,
there's the US standard atmosphere - changes every day - but we have a rough idea about what it is.
The problem with that is you can't get an analytical solution
from a solution like the standard atmosphere.
So we make an approximation to the atmosphere which is a isothermal model
which actually gives us a very simple exponential dependency of
density with altitude which enables us to solve the equation -
approximately but better than nothing. Really, it's just too useful approximation
to be able to ignore it. And
the error communicated in this plot here the blue - this nice straight blue line
on the logarithmic plot is our approximation we're going to make.
The red line is of course the real world, so it's a very significant differences
because we hide the differences a bit by making it a log plot,
but it's still a very useful approximation. But whenever you use it,
remember it is an approximation and check your numbers more carefully
before you hop into your spacecraft and fly.
Okay crunching the numbers a little bit you get down to a
nice solution which is velocity against altitude in terms of
how fast you started with, what your flight angle is and what you're aerodynamic characteristics
are - a very useful formulation.
That of course can now be analysed a bit further to work at what is your
deceleration at any point in time or point in altitude, so you could work out the stresses,
you got to design your vehicle to survive as well.
And then you can find out where your maximum deceleration occurs.
Very useful information that will be fairly well representative of
what's going to happen in flight.
Like if you've been out in space and you want to get home in a hurry, so
obviously the quickest way down is straight vertically down.
So what happens if you do that? You put π/2 (90 degrees) into your equations
and you'll see on that purple line there, you get a maximum acceleration of
about 180 G. You won't survive, so self-evidently you'll not be coming straight down.
What might be a more realistic angle to take? Well take this at 0.2 radians
for this condition where it's 8 km/s re-entry.
I've concocted some characteristics for a representative flight vehicle,
here's it's a bit more reasonable, we are coming in at around about 12 degrees and we're
peaking out at about 35-G. Still a bit too much for humans
but some payloads will be required to sustain those sort of decelerations.
So this is an example as to how you can control your trajectory compared - in the light of -
what are your objectives. Are you carrying people , are you carrying animals,
etc? Okay that was talking about coming back from Earth.
I'll now talk about a cruise corridor. This is , something we want to do when we get
scramjets working because you don't want to just go into space,
you want to keep traveling around the Earth, have a useful form of transport.
Well evidently if you're going at cruise - that's constant speed, constant altitude,
all your forces have to be matched.
So lift and drag have to be - sorry thrust and drag have to be matched
and also the more important thing to determine where to fly
is you need a certain centripetal force to keep going in a circle.
That comes partly from gravity, partly from the lift of your vehicle, so you can do a
simple formulation to relate these and that tells you where to fly for a given speed.
Of course now if you want to sustain cruise, drag is no longer an advantage
it's a disadvantage, so your vehicle shape has to change fundamentally.
You want slender bodies that look a bit nicer. This is a Darpa Falcon HTV-2 vehicle
which is non-manned experimental hypersonic aircraft which was flown recently.
It's sharp and you can see its sharp leading edges lead to high heat transfer so
a lot of disadvantages or problems you might say associated with
the use of them. This is another lifting body, you need to get lift
if you're going to cruise - this is a WaveRider tested in our expansion tube X3 at UQ.
They're long and slender, they look more like a traditional airplane in fact
and even the space shuttle when it comes close to touching down, it's flying again like
a proper airplane and it's not got it's 45 degrees angle of attack.
Okay, well how do we work these things out - very simple; the mass is pulling down, lift is
lifting you up with the difference between these makes you keep flying in a circle.
It's convenient to reference these speeds to what you would have
if you were in orbit. Like you go from the ground to orbit, you don't actually change
your altitude very much - about 100 kms out
of 6,400 radius of the Earth, so we'll ignore for the purposes of this analysis
any changes in g (gravity), take g to be constant. So we know that
can define what our orbital speed is, it's just g is V^2 over R.
So now we can write our equations including our lower speed where
you need to use your lift to hold you up there. And we'll reference everything
to your velocity you're flying with, that's the V, and the velocity you would have
in orbit and of course the lift coefficient in area and your density and your dynamic pressure.
We can extract the density from this and define at what density
you need to fly at to cruise it at given velocity. Why we want to know density?
Well once we've defined density, we can find out what altitude we have to fly at to get
that density and again we need re-invoke our abstract model
for density. Okay well you can solve that equation and you get a simple expression
for altitude. At this point of time I haven't put in a value for density,
if you substitute into this equation -
isothermal approximation for density which gives us the exponential dependency,
you can get this expression for altitude as a function of velocity.
Or you can do it the other way around to find what speed you need to fly at a given altitude
to cruise. Inspecting this equation, you can see
m/A - that's mass per unit area is an important parameter. We know that
as a ballistic coefficient of the vehicle, how heavy you're going to load its
wings. So on here I've plotted several ballistic coefficients to see how our flight
corridor changes in respect as you change your vehicle characteristics and you can see
over velocity range on horizontal axis coming in from Earth
orbit, you'll be bit under 8 km/s.That's where you're likely to be flying
in a lifting body trajectory.