Aircraft performance depending on gravity, air density etc.

[agent009]

Having seen quite a few speculations about use of different types of aircraft on different worlds, decided to do a little analysis on how this stuff really works. Enjoy!


AEROSTATS

Any object in a presence of a strong gravity field is subject to its attraction. The force acting on the object as a result of this attraction is called weight and defined as following:

W = m·g

where W is weight, m is mass of the object and g is gravity acceleration. The vector of weight is always directed toward the center of gravity.

However, if a solid object is immersed into a some fluid (either liquid or gas) under such conditions, it becomes a subject to another force, known as buoyant force – this force is equal in magnitude to the weight of the displaced fluid and directed away from the center of gravity:

B = Wdisp = mdisp·g = ρf·Vdisp·g

where B is buoyant force, Wdisp is weight of the displaced fluid, mdisp – mass of the displaced fluid, ρf – volumetric density of the fluid and Vdisp – volume of the displaced fluid.
Since buoyant force and weight are acting in opposite directions, they partially or totally cancel each other and net result of their action is known as effective buoyancy:

Be = B – W

The object is said to be at hydrostatic or aerostatic equilibrium when Be = 0, which can also be expressed as:

ρf·Vdisp·g - mo·g = 0

where mo is mass of the object. Since g is constant and non-zero, this means:

ρf·Vdisp = mo

If we assume that the object is completely immersed into the same fluid, then the volume of the displaced fluid would be equal to the volume of the object. Since mean density of the object is defined as ρo = mo/Vo (where Vo is volume of the object), the above hydrostatic/aerostatic equilibrium equation can be expressed as following:

ρf = ρo

As we can see, it is a matter of simple equity of densities. But as long as the state of equilibrium is not achieved, the object shall be subject to non-zero Be which shall either push it away from the center of gravity (if positive) or toward the center of gravity (if negative). Since density of fluid is proportional to its pressure under constant temperature and pressure of the mass of fluid tends to increase toward the center of gravity, the object would eventually achieve its hydrostatic/aerostatic equilibrium unless it is stopped by a physical obstacle or emerges from the of fluid before this happens.

On Earth, density of atmospheric air is significantly lower than that of any solid or liquid substance – therefore, most solid objects immersed into such atmosphere are subject to negative Be, nearly equal in magnitude to their weight. In order to take advantage of the buoyant force, one needs to construct a vehicle with mean density equal to that of atmospheric air at the target altitude. Such vehicles are collectively known as aerostats and decrease of mean density is accomplished by trapping inside a balloon some gas with lower density then air under the same ambient pressure. Lifting efficiency of an aerostat may be described in terms of effective mass of the vehicle (without the mass of lifting gas) at which it is able to achieve aerostatic equilibrium at target altitude. Thus:

m0 = B/g - mL = ρair·Vdisp - ρL·VL

where m0 is mass of the aerostat without lifting gas, mL – mass of the lifting gas, ρair – density of air at the target altitude, Vdisp volume of air displaced by the aerostat, ρL – density of the lifting gas at target altitude and VL – volume of the lifting gas at target altitude.

Density of a gas can be calculated as following:

ρ = p·M/(R·T)

where p is pressure, M – molar mass, T – temperature and R – the ideal gas constant. Thus:

m0 = pair·Mair·Vdisp/(R·Tair) - pL·ML·VL/(R·TL)

Assuming lifting gas is maintained at the same pressure and temperature as ambient air:

m0 = p·(Mair·Vdisp - ML·VL)/(R·T)

As long as the mean density of materials used to construct the aerostat is significantly higher than density of ambient air, most of the volume of air it displaces would be the volume occupied by the lifting gas, thus:

m0 ≈ p·VL·(Mair - ML)/(R·T)

This can also be expressed in terms of volume of the lifting gas required to lift certain mass:

VL ≈ m0·R·T/(p·(Mair - ML))

As we can see, lifting efficiency of an aerostat is directly proportional to its volume, atmospheric pressure and difference between molar masses of ambient air and of lifting gas, as well as inversely proportional to the ambient temperature. Gravity has no direct impact on – under the same atmospheric conditions, the same aerostat would be equally efficient regardless of gravity acceleration value. In fact, higher gravity would provide some indirect benefits for aerostats in terms of higher accent/descent acceleration and lower altitude pressure variations.

Therefore, aircraft relying primarily on aerostatic buoyancy would be most efficient on worlds with dense atmosphere, preferably consisting of heavy gases. Hydrogen could still be a quite efficient lifting gas in a helium atmosphere with sufficiently high pressure. However, in an atmosphere consisting primarily of hydrogen, only heated hydrogen or vacuum could provide reasonable aerostatic performance.


AERODYNAMIC AIRCRAFT

As soon as a solid object submerged in a fluid comes into motion, it becomes subject to additional forces. First of those is drag – it a vector opposite to the direction of motion and is calculated as following:

D = ρair·v²·XD(OG,AOA,p,T,SPf)

where D is the drag force, v – velocity of the object in relation to surrounding fluid and XD is a complex function of object geometry (OG) and angle of attack (AOA), as well as of temperature (T), pressure (p) and specific properties of the surrounding fluid (SPf).

The second aerodynamic/hydrodynamic force is known as lift, which may be calculated following:

L = ρair·v²·XL(OG,AOA,p,T,SPf)

where L is the lifting force and XL is, again, a function of object geometry and angle of attack, as well as of temperature, pressure and specific properties of the surrounding fluid (not the same as XD). This force is used by winged aircraft and flying animals to achieve flight, but it can be act in any direction perpendicular to the axis of motion depending on the shape of the object – not necessarily against the vector of gravity. Rudders of both aircraft and watercraft use the same force to control the horizontal direction and fore-and-aft rigged sailing vessels convert the lift produced by the flow of wind against the sail into forward thrust (square rig, on the other hand, takes advantage of the drag). Cetaceans and rays use the lift of water both to ascend above their hydrostatic equilibrium and to submerge below it.

Finally, in order to achieve forward motion, one needs thrust. In most cases it is produced by power input – either by artificially producing drag (oars and paddles) or lift (fins, screws, propellers, turbofans etc.) forces, or by reactive jet propulsion (rocket engines, turbojets, water jets of squids and octopuses). Sailing vessels, gliders and soaring birds are taking advantage of aerodynamic forces produced by wind in order to achieve thrust.

Now, if we consider a powered dynamic aircraft (which may or may not additionally rely on aerostatic buoyancy), in order to achieve flight the following must be true:

W ≤ B + L

where W is overall weight of the aircraft, B – buoyant force and L – net vector of aerodynamic lifting forces acting against the vector of weight. When W = B + L the aircraft achieves its aerodynamic equilibrium. The above applies to both heavier-then-air aircraft and powered aerostats (airships) since any object moving in a fluid shall be subject to both buoyancy force and aerodynamic lift to some extent. Buoyancy effect is however negligible for most winged aircraft as their mean density is greater than that of ambient air by several orders of magnitude, thus, for this type of aircraft, we could assume the aerodynamic equilibrium would occur when W = L. The mass with which an aircraft of specific configuration could achieve aerodynamic equilibrium could be expressed as following:

m0 = ρair·v²·XL(OG,AOA,p,T,SPf)/g

As we can see, efficiency of an aircraft relying solely on dynamic lift is directly proportional to the density of atmospheric air and to square of its airspeed, while it is inversely proportional to the gravity. This means, the same airplane or helicopter would perform twice better than on Earth under 0.5g and twice as poorly under 2g (all other things being equal).

Increased atmospheric density appears to give an advantage too, but let us not forget that it would also increase drag by the same magnitude. In order to achieve the desired airspeed the aircraft must convert some amount of power into thrust, and part of this power would be required to overcome the drag, which is calculated as following:

PD = ρair·v³·XD(OG,AOA,p,T,SPf)

where PD is power input needed to overcome drag. So, an increase of density Δρ would increase the amount of lift available by factor Δρ, but it would also increase the amount of power needed to overcome the additional drag at given airspeed by factor Δρ·v. Yes, higher density would give better lift at lower airspeed but would also increase the amount of energy required to achieve higher airspeed – since airspeed has much greater impact on the lifting performance then air density, this is not necessarily an advantage. For airplanes, denser air would be an advantage during take-offs and landings, but it would significantly decrease their fuel efficiency during cruise.

For helicopters it would likely be an advantage since they burn much more fuel for lift then for thrust and rotor blades do not need to overcome as much drag as the airplane body. A helicopter could spin its rotor at lower throttle to achieve the same amount of lift or could use shorter blades, which would reduce airspeed difference between base and tip of the blade and make the lift more uniform (which could actually provide better fuel efficiency). This would also reduce dissymmetry lift during forward flight and “never exceed” speed limit (though power input needed for forward thrust would still be increased).


CONCLUSION

Performance of aerostatic and rotary wing aircraft would clearly improve in denser atmospheres, but advantage for fixed-wing aircraft is questionable. While performance improvement of aerostats in denser atmospheres would greatly depend on atmospheric composition, it would not matter for winged aircraft whether density increase comes from pressure, molar mass or temperature. While performance of heavier-then-air aircraft would greatly benefit from lower gravity and greatly suffer from higher gravity, this would have no direct impact on performance of aerostats (there might be even some indirect benefits from higher gravity).

[Ziggy Stardust]

What about fuel and fuel efficiency? Theoretically, wouldn't pressure and gravity affect these in a variety of ways? The amount of fuel that can be piped through the fuel lines in a given period of time, the net energy content of the fuel per unit volume, etc? I know modern aircraft fuel tanks are vented to prevent fuel starvation, which allows for a greater degree of resistance to changes in pressure and temperature, but presumably these are calibrated to Earth atmospheric levels. Would the design of the tank vents necessarily have to change in a non-Earth atmosphere?

[agent009]

What about fuel and fuel efficiency? Theoretically, wouldn't pressure and gravity affect these in a variety of ways?

Fuel efficiency, just like lifting efficiency of heavier-then-air aircraft would be inversely proportional to gravity, since they rely on dynamic lift produced by power input. Fuel efficiency of airships, on the other hand, will be completely unaffected by gravity as they rely on aerostatic buoyancy for lift (on which, as I have demonstrated, the magnitude of gravity has no direct impact) and only need thrust to produce forward momentum.

As I have mentioned, increase of atmospheric density would have an overall negative impact on fuel efficiency of fixed-wing aircraft (i.e. airplanes) due to increased drag (you get much more "bang" out of airspeed increase then out of air density increase during cruise - that's why commercial airliners and business jets like to fly so high), but might improve it for short-range low-airspeed flights (more lift per airspeed means fuel economy during take-offs). Rotary wing aircraft (i.e. helicopters) on the other hand, would likely have greater fuel efficiency in a denser atmosphere, as it would mean lower airspeed/AOA of rotor blades and more uniform lift (rotor blades have relatively small cross-section and effect of increased drag would be marginal compared to the effect of increased lift). They would still need to overcome more drag during forward flight but, unlike airplanes, helicopters do not gain any fuel efficiency advantages from flying faster and their maximum airspeed is still limited by the dissymmetry of lift. While for airships increased drag would mean increased fuel consumption, this would be largely offset by decreased volume of lifting gas required to lift the same mass and thus, smaller cross-section area of the hull (= decrease of drag). Again, drag is much less of a factor at lower airspeeds, at which airships normally cruise.

The amount of fuel that can be piped through the fuel lines in a given period of time, the net energy content of the fuel per unit volume, etc?

Liquid fuel (as is the case with most liquids) has relatively low compressibility and the impact of ambient pressure on its density is rather minor (there won't be any drastic changes in J/L ratio). Pressure and/or gravity increase would likely increase throughput of pipelines - I'm unsure how much impact this would have on fuel efficiency but, probably, not that much, compared to the effects of increased/reduced lift/drag. Gaseous fuel could become more interesting with increased pressure (lighter tanks for liquefied gas).

I know modern aircraft fuel tanks are vented to prevent fuel starvation, which allows for a greater degree of resistance to changes in pressure and temperature, but presumably these are calibrated to Earth atmospheric levels. Would the design of the tank vents necessarily have to change in a non-Earth atmosphere?

Changes in atmospheric pressure and composition would likely have a significant impact on the design of those vents, but I haven't really done much research on that subject, so I'm not sure what exactly such changes would entail.

[agent009]

Some more thoughts on this.


SPEED OF SOUND

Speed of sound is an important consideration for performance of aircraft relying primarily on dynamic lift, as performance of the same aircraft would vary significantly depending on whether its airspeed is below or above the speed of sound in a given environment. In fact, there would be two sets of XL and XD relations I’ve mentioned earlier for each aircraft design – one for subsonic regime and another (completely different) for supersonic airspeeds. There is also a mixed “transonic” regime, which occurs when the speed of airflow is just around the speed of sound – in this state, some local airflows may exceed the speed of sound while others will remain subsonic (which would, again, give you a different set of XL and XD). The speed of sound may be determined as following:

vs = √(T/(M/R - M/cp))

Where T is the temperature of the fluid, M – mean molar mass of the fluid mixture, cp – heat capacity under constant pressure and R – the ideal gas constant. This may be also expressed as following:

vs = √(qvs∙T) where qvs = 1/(M/R – M/cp)

Since M and cp are constant for any given chemical compound or mixture and R is constant by definition, the speed of sound factor qvs would also remain constant, while T will be a variable magnitude. Thus, when comparing different compositions of atmosphere, greater qvs would mean greater speed of sound at the same temperature. For vast majority of gases, greater values of M result in smaller values of qvs (water is a notable exception – it has lower molar mass then neon, but also significantly lower speed of sound factor due to its unusually high heat capacity). As a general rule, high molar fractions of “light” gases (e.g. H₂, He) mean higher speed of sound, while significant fractions of “heavy” gases (e.g. SF₆, CO₂, Xe, Kr) will considerably lower it.


HOT AIR AND LOW PRESSURE BALLOONS

In my initial post, I have described the efficiency factors for aerostats relying on lower molar mass of the lifting gas (compared to ambient air) to achieve buoyancy. Such aerostats are usually the most practical, but this won’t work very well in the atmosphere with high molar fraction of hydrogen (since no stable chemical compound has lower molar mass the H₂). Let’s recall the formula of aerostatic equilibrium:

m0 = (pair·Mair·Vdisp/Tair - pL·ML·VL/TL)/R

So, if we have Mair ≈ MH₂ and, since Vdisp ≈ VL as long as the density of air is significantly lower than that of any solid substance, we only have two other variables to play with – pL and TL. As our goal is to maximize m0, we would either have to increase the temperature of the lifting gas or decrease its pressure. If we decide to play with the temperature, we get a hot-air balloon, and the above formula would look like this:

m0 = (p·M·V/R)·(1/Tair – 1/TL)

As we can see, the efficiency of a hot air balloon is directly proportional to pressure and to molar mass of the air. However, we would still get more efficiency out of molar mass difference principal as long as our atmosphere is “heavier” then helium. However, such balloons could still be quite efficient in high-pressure hydrogen/helium atmospheres.

But let us consider lowering pressure rather than rising temperature instead. This would give us:

m0 = M·V·(pair - pL)/(R·T)

Since theoretical minimum for pL is 0 (vacuum) this appears to be a very attractive way to achieve aerostatic buoyancy, as lifting efficiency for a “vacuum balloon” would be:

m0 = M·V·pair/(R·T)

However, let us not forget that in order to maintain lifting gas below ambient pressure requires require a solid “balloon” strong enough to withstand the structural stress of pressure difference. This would mean additional mass. So let Δp = pair - pL and Δm be the increase of mass needed to sustain such stress (which would be a function of V and Δp). Thus, we would have following equation:

m0 = M·V·Δp/(R·T) - Δm(V,Δp)

In order to achieve positive buoyancy, there must be some values of V and Δp when m0 > 0. I.e.:

M·V·Δp/(R·T) > Δm(V,Δp)

It has been proven empirically that such a relation is not possible for any known materials unless the value of M is very high or the value of T is extremely low, but no known substance could exist in gaseous state under such conditions (the above formula only holds true for gases, since density of liquids is subject to different relations). The only examples of “low-pressure balloons” are submarines where air in the crew living spaces (which acts as lifting gas) is kept below ambient pressure of the outside fluid. However, this is done mainly for the benefit of the crew, and in fact, the requirement of a strong heavy hull able to withstand such pressure difference deteriorates hydrostatic performance. Unless some new extremely light and extremely strong material is discovered, “low-pressure balloons” or “vacuum balloons” would not be practical in a gaseous environment.

[Broomstick]

Performance of aerostatic and rotary wing aircraft would clearly improve in denser atmospheres, but advantage for fixed-wing aircraft is questionable.

As an actual pilot I have to dispute this one.

Increasing density DOES have a notable effect on the performance of a fixed wing aircraft, so much so that pilot's on Earth have to take into account the effect of temperature, altitude, and humidity (water vapor is less dense than most of the other atmospheric gasses for Earth so the higher proportion of water vapor the less dense the air in a region will be) on air density while flight planning.

As a couple illustrations, using the exact same plane under the same loading (me along plus full fuel) I have personally observed that taking off from the same runway in winter make take a third of the required distance as using the same runway in summer. That is quite a significant difference from a relatively small change in density compared to some of what we're considering here.

True, higher density does result in higher drag and burn more fuel, but there are trade-offs here because getting around isn't just about fuel burn. There are also design considerations regarding airfoils optimized for low-density, cruising, heavy lifting, and speed all of which have their own trade-offs and benefits.

If you're flying on Mars you're going to need a radically difference airfoil than flying on Venus. Have you taken that into account in your calculations? You would need to optimize both fixed wing airfoils and rotorcraft to, say, Venus conditions THEN make a comparison between them.

[Broomstick]

And... past the edit window but let me clarify my remarks a bit more.

Yes, your calculations do take into account what I mentioned above, but what I mean is, what is the CONTEXT of your flying? For sample retrieval greater efficiency in ascending may be an important factor. Rotorcraft have FAR more moving parts than fixed wing aircraft and are much more likely to break down, and require more maintenance - how important is durability and reliability? There are a lot of different factors that go beyond just an equation. What you're using the aircraft for makes a significant difference, that's why the modern world still uses both fixed wing and rotary aircraft as they have different uses.

[agent009]

Increasing density DOES have a notable effect on the performance of a fixed wing aircraft, so much so that pilot's on Earth have to take into account the effect of temperature, altitude, and humidity (water vapor is less dense than most of the other atmospheric gasses for Earth so the higher proportion of water vapor the less dense the air in a region will be) on air density while flight planning.

That does not actually contradict with what I wrote:

Yes, higher density would give better lift at lower airspeed but would also increase the amount of energy required to achieve higher airspeed – since airspeed has much greater impact on the lifting performance then air density, this is not necessarily an advantage. For airplanes, denser air would be an advantage during take-offs and landings, but it would significantly decrease their fuel efficiency during cruise.

and

As I have mentioned, increase of atmospheric density would have an overall negative impact on fuel efficiency of fixed-wing aircraft (i.e. airplanes) due to increased drag (you get much more "bang" out of airspeed increase then out of air density increase during cruise - that's why commercial airliners and business jets like to fly so high), but might improve it for short-range low-airspeed flights (more lift per airspeed means fuel economy during take-offs).

What I meant by "questionable" is that there is no clear overall advantage or disadvantage. Higher air density = greater fuel burn on long flights vs. better take-off/landing and low airspeed performance.

If you're flying on Mars you're going to need a radically difference airfoil than flying on Venus. Have you taken that into account in your calculations? You would need to optimize both fixed wing airfoils and rotorcraft to, say, Venus conditions THEN make a comparison between them.

Well, I can hardly do any math on that until such aircraft have actually been built, since lift and drag coefficients for specific aircraft design under specific flight conditions can only be determined empirically As far as I can judge, for rotorcraft main design changes would relate to configuration and throttle range of the main rotor(s). For fixed-wing, lifting body design might make sense for denser atmospheres, while for significantly less denser atmospheres multi-plane configuration might be necessary to achieve flight. Again, as I mentioned, it would also depend very much on the magnitude of g.

Yes, your calculations do take into account what I mentioned above, but what I mean is, what is the CONTEXT of your flying?

Mostly just an intellectual exercise Basically, my research was for my literary sci-fi work, so I was trying to get some idea how different types of aircraft would work on worlds with gravity/atmospheric conditions radically different from Earth.

[slebetman]

Well, I can hardly do any math on that until such aircraft have actually been built, since lift and drag coefficients for specific aircraft design under specific flight conditions can only be determined empirically As far as I can judge, for rotorcraft main design changes would relate to configuration and throttle range of the main rotor(s). For fixed-wing, lifting body design might make sense for denser atmospheres, while for significantly less denser atmospheres multi-plane configuration might be necessary to achieve flight. Again, as I mentioned, it would also depend very much on the magnitude of g.

Actually, with regards to airfoil, you can simulate both using CFD software. In fact, RC aircraft designers (especially competition glider designers) essentially design aircraft for flight in a higher atmospheric pressure. They design and simulate their planes to fly at very low Reynolds numbers. That's because Re numbers are proportional to wing chord and inversely proportional to air viscosity. So designing an airfoil for a small toy plane is the same as designing an airfoil for a normal plane to fly in a more dense atmosphere (OK, viscosity is not the same as density but viscosity and density are proportional for air. Still, if the alien atmosphere has different composition it's possible to have higher than earth density but lower than earth viscosity).

If you just want to play with this stuff (that is, if you don't intend to build a human carrying aircraft) then most hobbyist designers use a program called xfoil to do the CFD simulation. If you want to simulate the whole plane then take a look at xflr5. Both are used by high end RC glider and pylon racer designers.

[agent009]

Actually, with regards to airfoil, you can simulate both using CFD software.

Airfoil geometry is not the only thing which affects lift. For one thing, as you correctly mentioned, there is viscosity, which could be very different for different gas mixtures. Then, there is planform area, AOA, wing sweep, Mach number (v/vs) and a number of other factors. The exact exact relations between all those things are not completely understood and usually determined experimentally, as far as I could gather from the sources I have read, so I just prefer to describe those relations as a "black box" XL function in my simplified model. At any rate rate, the purpose of my study was not so much to design an aircraft for specific planetary conditions, but to understand the general principle how the main variables of those conditions would affect performance of an aircraft of any given design.

[agent009]

I should probably explain this a little more... in my dynamic lift equations, I use XL to describe the AW·CL/2 relation, where AW is the planform area (basically wing area for most fixed-wing aircraft designs) and CL is what is usually known as lifting coefficient. If we apply the Thin Airfoil Theory, CL = 2πα + CL0, where α is the angle of attack (AOA) and CL0 is the CL at zero AOA (the amount of lift produced by the actual airfoil shape and wing configuration, which is related to the Reynold's Number as well as to Mach Number at airspeeds approaching or exceeding the speed of sound. This means:

XL = AW(πα + CL0/2)

and

L = ρair·v²·AW(πα + CL0/2)

As we can see, the planform area AW and the angle of attack α have the most significant impact on the dynamic lift compared to other relations defined by XL (hence, any piece of plywood would fly given enough airspeed and right AOA). It must be noted however, that there is a maximum value of AOA which is known as stall point, beyond which further AOA increase will lead to complete loss of lift (around 10° - 15° for most typical airfoils). Also note that greater AOA means greater drag.

[Broomstick]

The exact exact relations between all those things are not completely understood and usually determined experimentally, as far as I could gather from the sources I have read, so I just prefer to describe those relations as a "black box" XL function in my simplified model.

They're well enough understood to utilize that theory in design, then use real-model testing to confirm the results and/or tweak them. You can make some educated guesses as to what would or wouldn't work.

[agent009]

They're well enough understood to utilize that theory in design, then use real-model testing to confirm the results and/or tweak them. You can make some educated guesses as to what would or wouldn't work.

Mind posting a formula for computing the lifting and drag coefficients as functions of aircraft geometry, airspeed, air density, Reynold's Number and Mach Number as well as a formula for computing viscosity of an arbitrary gas mixture (which would be needed for computing the Reynold's Number) that would not require empirically determined parameters then? I was not able to find any such formulas so far.

[Elheru Aran]

Could you not simulate the various necessary coefficients by making a big old wind tunnel that's airtight and can be pressurized, then introduce the various atmospheric mixes and go from there? The only thing lacking would be gravity and you can allow for that with some math, can't you?

(Disclaimer: This is not my field, that's just the solution that came to mind)

[Broomstick]

They're well enough understood to utilize that theory in design, then use real-model testing to confirm the results and/or tweak them. You can make some educated guesses as to what would or wouldn't work.

Mind posting a formula for computing the lifting and drag coefficients as functions of aircraft geometry, airspeed, air density, Reynold's Number and Mach Number as well as a formula for computing viscosity of an arbitrary gas mixture (which would be needed for computing the Reynold's Number) that would not require empirically determined parameters then? I was not able to find any such formulas so far.

For better or worse, I am strictly an empirical pilot. Give me an aircraft and I can fly it, I know enough match to do what's required for weight and balance, navigation, and Earth-based weather calculations, but I can't do the advanced math required for the theoretical design work. From your posts, I'm assuming your knowledge of aviation is theoretical and mathematical, not empirical. Nothing wrong with either approach, they both have strengths and weaknesses.

We have at least one honest-to-goodness aerospace designer on this board, or at least we did. It wouldn't surprise me if someone happens along with the equations. If I have some time I'll look in some of my more advanced flight school information and see if I can help direct you towards the appropriate equations.

My empirical experience tells me that there are some rules of thumb to follow in aircraft design - hence whey you see long, thin wings typically proposed for martian aircraft. For really dense, viscous atmospheres things will trend more towards submarines, which do in fact "fly" under water, needing to account for drag and dive planes utilizing lift when maneuvering the boat. There's a significant overlap between aviation and marine design concerns.

Fixed wings in a thin atmosphere will trend towards long and thin - see the U2 spyplane or Helios solar design. There are exceptions to that, like the SR-71 blackbird but that one was intended for trans-sonic speeds, which favor swept wings, low drag, and other traits. Fixed wings in a very dense atmosphere will trend towards short and stubby to reduce drag in an environment where lift generation is fairly easy. For an extreme example, look at the size of dive planes and rudder on a submarine compared to those on an airplane.

I'm not at all an expert on rotorcraft, but as long as you remember the rotors are airfoils similar principles should apply.

[Broomstick]

Could you not simulate the various necessary coefficients by making a big old wind tunnel that's airtight and can be pressurized, then introduce the various atmospheric mixes and go from there? The only thing lacking would be gravity and you can allow for that with some math, can't you?

NASA has done some work along those lines, and they make quite a bit of their data available to the public if you want to do the looking.

As a bit of trivia - if you watched the Avengers movie that big space they filmed the tesseract and Loki's arrival in is, in fact, a pressure vessel owned by NASA for doing that sort of work. It is not, however, a facility open to hobbyists

[agent009]

My empirical experience tells me that there are some rules of thumb to follow in aircraft design - hence whey you see long, thin wings typically proposed for martian aircraft. For really dense, viscous atmospheres things will trend more towards submarines, which do in fact "fly" under water, needing to account for drag and dive planes utilizing lift when maneuvering the boat. There's a significant overlap between aviation and marine design concerns.

Well, for once, as you mentioned, air viscosity (more specifically, kinematic viscosity) becomes an important factor at high airspeed. While it has a direct relation to density, it is also a function of dynamic viscosity, which may be quite different for different gas mixtures under different temperature/pressure conditions. While constants needed to calculate dynamic viscosity for most pure gases are relatively well known, unlike with molecular mass and heat capacity, dynamic viscosity of a mixture will not be simply a weighted average of its fractions - there is no easy way to determine what this value will be except by actually creating a comparable mixture in a lab and measuring its parameters. Unfortunately, I do not have access to facilities that would be required to do that.

Fixed wings in a thin atmosphere will trend towards long and thin - see the U2 spyplane or Helios solar design.

Makes sense, since you would need larger planform area to achieve the same lift at the same airspeed. But since lower air density would mean less structural stress, you can make them thiner and, hence, lighter.

There are exceptions to that, like the SR-71 blackbird but that one was intended for trans-sonic speeds, which favor swept wings, low drag, and other traits.

Yes, at transonic/supersonic speed you have an added factor of wave drag. Also, supersonic and subsonic airflows do not act the same way on an airfoil, so different design principles apply.

Fixed wings in a very dense atmosphere will trend towards short and stubby to reduce drag in an environment where lift generation is fairly easy. For an extreme example, look at the size of dive planes and rudder on a submarine compared to those on an airplane.

Yep, smaller planform area, but more drag and structural stress. But yep submarines are a bit of an extreme example - in order to have even half the density of water in a gaseous environment you would need to put some very heavy gases under very high pressure (e.g. about 100 ATA of pure SF₆ would give you roughly half the density of liquid water) - but normally, atmospheric density would be by several orders of magnitude less then that of most liquids.

I'm not at all an expert on rotorcraft, but as long as you remember the rotors are airfoils similar principles should apply.

Yes, for rotorcraft, rotor blades are the main lift-generating planforms. A big difference with fixed-wing is that airspeed of your "wing" is not the same thing as the airspeed of the aircraft itself and rotorcraft suffer from an effect known as dissymmetry of lift at high airspeeds - i.e. true airspeed of the advancing blade becomes much higher then that of the retreating blade. This is compensated by adjusting AOA of the blades, but at certain airspeed of the aircraft, you will either have your retreating blade at maximum AOA (stall point) or your advancing blade would become supersonic. And then, the longer your blade is and the faster you spin the rotor - the more airspeed difference there would between the base and the tip of the blade. Lengthening the blades too long or increasing spin rate in thinner atmospheres might not work as you would risk the tips of the blades becoming supersonic before you could achieve the required amount of lift - so you would like need multiple rotors. In denser atmospheres you would either spin the rotor slower or make the blades shorter, which would improve the overall performance.

[madd0ct0r]

I'm surprised no body has referenced here yet: http://what-if.xkcd.com/30/
I'm sure the calcs will be around the internet somewhere...

[MrDakka]

Mind posting a formula for computing the lifting and drag coefficients as functions of aircraft geometry, airspeed, air density, Reynold's Number and Mach Number as well as a formula for computing viscosity of an arbitrary gas mixture (which would be needed for computing the Reynold's Number) that would not require empirically determined parameters then? I was not able to find any such formulas so far.

You might want to look into some of the equations of lifting line theory shown in the links below. Mind you lifting line theory is based on the steady, incompressible, inviscid flow assumptions.

http://www.aerospaceweb.org/question/ae ... 0184.shtml
http://en.wikipedia.org/wiki/Lifting-line_theory
http://www2.esm.vt.edu/~dtmook/AOE5104_ ... ss_LLT.pdf
http://www.desktop.aero/appliedaero/pot ... gLine.html

[Broomstick]

Fixed wings in a thin atmosphere will trend towards long and thin - see the U2 spyplane or Helios solar design.

Makes sense, since you would need larger planform area to achieve the same lift at the same airspeed. But since lower air density would mean less structural stress, you can make them thiner and, hence, lighter.

The chord (distance from leading to trailing edge) of the airfoil also impacts drag. This is further complicated by most wings not having the same chord their entire length.

You see this in flying animals, too - birds that do a lot of gliding like albatrosses have wings with small chords, "power" flyers that need a lot maneuverability, like some of the raptors and forest-dwelling birds, have wings with large chords. The large pterodactyls also trended towards long, thin wings. With flying animals the larger the flyer the more that trend is evident. With smaller flyers you get shorter wings with shorter chords - look at hummingbirds and bees. While organic flyers have some constraints mechanical ones don't there are reasons for these trends. People either don't consider or forget that for something the size of a bee how it experiences air is a lot different than how we do.

I found this link, not sure how helpful you'll find it.

[Elheru Aran]

So an airplane for a dense gas environment might resemble, oh, the F-104 Starfighter, just with more of a lifting-body fuselage? I could get behind that, I always dug the 104...

[Sea Skimmer]

Engine design would get interesting, given that modern turbine engines are already limited by inlet temperature, and since that's a more or less fixed value higher exhaust pressure means the overall allowable pressure ratio will have to go down. While That means considerably less efficient engines unless you can find other ways to compensate, such variable bypass engines to improve high altitude performance without exploding at a sea level takeoff. Even that has limits though. Less power will be needed for the compressor, but you can only save so much on that since you still need maximum power for takeoff at low speed at high altitude runways. Which I imagine can now be higher then any point on earth actually is.

On the other hand a ramjet might get really damn effective at lower speeds then currently considered useful. Turbo-ramjets could have a lot of appeal.

[Sky Captain]

Engine design would get interesting, given that modern turbine engines are already limited by inlet temperature, and since that's a more or less fixed value higher exhaust pressure means the overall allowable pressure ratio will have to go down. While That means considerably less efficient engines unless you can find other ways to compensate, such variable bypass engines to improve high altitude performance without exploding at a sea level takeoff. Even that has limits though. Less power will be needed for the compressor, but you can only save so much on that since you still need maximum power for takeoff at low speed at high altitude runways. Which I imagine can now be higher then any point on earth actually is.

On the other hand a ramjet might get really damn effective at lower speeds then currently considered useful. Turbo-ramjets could have a lot of appeal.

Would similar problem also affect piston engines? In a dense atmosphere propellers would become more effective and if jet engines become hard to build and inefficient then piston engine powered propeller aircraft may be better if you don't need to fly very fast. Maybe have few piston engines with foldable propellers to assist jets in sea level takeoff and once climbed to enough altitude where jets become efficient shut down piston engines fold the propellers and cruise fast on jet thrust.

[Purple]

If you want something to assist in takeoff why not just JATO it? As in, strap a few rockets under your wings to bust you up to speed for takeoff and take you high enough for your engines to start working properly.

[Sea Skimmer]

JATO is expensive and dangerous, and higher pressure means the specific impulse of rocket motors goes down so it will be even more expensive here. If it proved to be a large enough problem aircraft would just end up carrying auxiliary takeoff engines in the style of the C-123K or some such I think. Simple, low drag things that can easily detach for maintaining or maybe even be taken off for flight profiles that don't need them.

Would similar problem also affect piston engines? In a dense atmosphere propellers would become more effective and if jet engines become hard to build and inefficient then piston engine powered propeller aircraft may be better if you don't need to fly very fast. Maybe have few piston engines with foldable propellers to assist jets in sea level takeoff and once climbed to enough altitude where jets become efficient shut down piston engines fold the propellers and cruise fast on jet thrust.

If the pressure was high enough you would run into the same problem of only being able to have a very low pressure ratio; but up to a certain point a piston engine would love higher intake pressure and is less affected by back pressure. I dunno where that line would be, air temperature would play a huge effect on it but you have to design for worst case takeoff. In real life we can make diesels that take 150psi of boost but if you start talking in terms of 20 atmospheres we've already hit double that as our static pressure.

Auxiliary folding rotor piston engines...this is complex as it comes. At that point it'd likely make more sense to build a propfan, or just put the folding rotors on a turboshaft that can operate as a turbojet at high altitude. Such engines have been studied. Though the British also did work on a turbo compounding piston engine that also had a secondary burner ahead of the turbine.... I have no idea what you call that. It didn't make it into production due to sanity being engaged.

[agent009]

Would similar problem also affect piston engines? In a dense atmosphere propellers would become more effective and if jet engines become hard to build and inefficient then piston engine powered propeller aircraft may be better if you don't need to fly very fast. Maybe have few piston engines with foldable propellers to assist jets in sea level takeoff and once climbed to enough altitude where jets become efficient shut down piston engines fold the propellers and cruise fast on jet thrust.

Propellers aren't really "more effective" in denser fluids. Well, they are in a sense that you could get away with lower AR blades and spin them faster without fear of the blade tips breaking sound barrier (though you must also consider what airspeed Mach 1 would actually correspond to in a specific atmosphere - e.g. it would be much higher in hydrogen and much lower in CO₂). But you would still need about the same amount of energy in order to accelerate the same mass of air to the same speed and achieve the same amount of thrust. So, in this respect, piston engines would not really be any more efficient then they are on Earth.

Important question is also what compounds you would actually use to produce the chemical reaction that drives any internal combustion engine. On earth, you carry hydrocarbonic fuel in the fuel tanks and make it react with oxygen (of which you've got lots in the atmosphere). On Titan, you would likely want to carry some oxidizer in your fuel tanks and make it react with atmospheric methane. Same on gas giants, except that your oxidizer "fuel" would react with atmospheric hydrogen rather then methane. On Mars and Venus you would need to carry both fuel and oxidizer aboard, since you've got no chemically reactive compounds in the atmosphere to speak of.