Calculating the hover height of the Harrier jet

[mooeypoo]

Hi guys,

 

I had a discussion with a friend about the Harrier jet and how far up it could go compared to the propulsion of the jet, and if we could calculate this mathematically.

 

Before I go on, the Harrier jet is a pretty cool attack plane that can lift off vertically. See example here:

 

 

Theoretically speaking, if instead of gas propulsion we had water jets going downwards (powerful ones) and we know the weight of the jet, we should be able to calculate at what distance above the ground the forces of the thrust from the propulsion equals the force of gravity from the plane's weight. So we could tell how far up it would go based on the initial pressure out of the nozzle.

 

I know this is possible to calculate, I'm just having trouble implementing this. How would I go about calculating it? If I want to build my own small model with garden hoses and a tiny jet (on a little plate or something), I would then have the exact pressure out of the nozzle of the garden hose, and the weight of the model plane + plate, how would I calculate how far up the model plane would go?

 

I'm a bit confused, I'm not sure how to start this. Bernoulli's equation doesn't seem to help because it requires an enclosed flow and this is not one of those, so I went with jet propulsion equations, like in this resource form NASA. But that seems to speak about horizontal propulsion, and not quite about vertical one.

 

Any help? If we know initial pressure from the nozzles and weight of the model plane, how do you start calculating the equilibrium equation?

 

Thanks!

 

~mooey

[Cap'n Refsmmat]

I'm not sure I understand your question. If your jets push out a specific mass at a specific velocity, their thrust is constant, independent of altitude. You can rise as high as you want. The practical problems only come in when your engine thrust decreases due to thin air at altitude.

 

Harriers, for example, are known for entering hover at high altitude and high speeds to suddenly decelerate, causing a pursuing aircraft to overshoot and become vulnerable to missiles.

[pmb]

Hi guys,

 

I had a discussion with a friend about the Harrier jet and how far up it could go compared to the propulsion of the jet, and if we could calculate this mathematically.

The Harrier,or any plane like it, can just as easily hover at 50 feet as it can 500 feet. The only difference is the air pressure. All you need to do is calculate the thrust and set that equal to the weight of the Harrier. When these are the same then the Harrier is hovering. Note that the weight is constantly changing due to the fuel burning. So as time goes on the fuel decreases and with that the weight decreases.

 

Pete

Edited May 18, 2012 by pmb

[imatfaal]

Moooey - bit confused. What does height above ground have to do with it? Surely it's just a reaction in terms of newtons 3rd law - ie you throw/accelerate enough gas downwards, quickly enough then reactive force is enough to lift the plane upwards. Whilst there is enough air around you for the engines to scoop in and push downwards then the Harrier will keep working. With water jets this would not be a problem because - like a rocket - you are carrying your ejected matter with you.

 

I think I must be missing something - my gut instinct is that if the downward thrusts are enough to get the aircraft off the ground then the the aircraft will continue to rise until the thrust is reduced; ie there will be no point at which the forces are balanced, gravity will get very marginally weaker and the force from the engines will remain the same.

 

horrible feeling i am gonna crash and burn on this one - there was always a good reason I wasn't a fighter pilot

 

ok - so I crossed-posted with capn and pmb

[swansont]

For airfoil-based lift, i.e. a helicopter, there is a ground effect which allows you to be close to the ground with less power. Any equivalent for a Harrier-style thrust?

 

At a rotor height of one-half rotor diameter, the thrust is increased about 7 percent. At rotor heights above one rotor diameter, the thrust increase is small and decreases to zero at a height of about 1 1/4 rotor diameters.

http://www.copters.com/aero/ground_effect.html

[pmb]

For airfoil-based lift, i.e. a helicopter, there is a ground effect which allows you to be close to the ground with less power. Any equivalent for a Harrier-style thrust?

 

 

http://www.copters.c...und_effect.html

This airfoil-based lift - Does it have much affect at, say, 50 feet or 500 feet?

[mooeypoo]

Okay, let me organize my question better.

 

I want to recreate this effect in my back yard with garden hozes and a model airplane. Yes, I know that water is not the same as jet fuel gas, but the principle should be more or less the same -- force downwards lifting the little toy up. To make it balanced, I'll put the toy on a square plate and 4 hoses, one in each side, so it's more or less balanced. Let's ignore the balance for a moment though (theoretically speaking if all 4 hoses are equal, I hve equal forces on all sides, reality be damned)

 

Obviously, if I have a low stream in the hose nozzle (lower pressure coming out) the contraption will go to some relatively low height, and if I increase the flow (pressure through the nozzle) it will soar HIGHER. I know this from observation. I'm trying to see if I can calculate *how high* it can go based on how *strong* my flow is through the garden hose, knowing the mass of the toy plane.

 

Does this make sense?

[Joatmon]

The link doesn't answer your question - but does indicate the idea is feasible

http://www.wired.com...-a-single-tank/

 

The attachment may give you some help (from the second link)

 

http://en.wikipedia....ing_Peak_Height

Edited May 18, 2012 by Joatmon

[ewmon]

The force of gravity on the mass of the airplane won't change appreciably with altitude, but the density of the air (which also depends on the weather), and the amount of fuel that burns with it, is the main factor that determines how much thrust engines can produce as shown by the thrust "map" below.

 

Keep in mind that, for example, "hovering" that might occur at 12km at high speed mostly allows the drag to slow the plane very quickly without requiring any energy-dumping maneuvers. You'll start to drop, but you have some altitude to spare at 12km, besides all you want to do is suddenly drop back in level flight, then you're back flying like an airplane again.

 

As for actual hovering, I suspect that you can't do that at any appreciable altitude. This webpage suggests that its "hover ceiling" is about 5,000ft/1,500m.

 

[Cap'n Refsmmat]

Obviously, if I have a low stream in the hose nozzle (lower pressure coming out) the contraption will go to some relatively low height, and if I increase the flow (pressure through the nozzle) it will soar HIGHER. I know this from observation. I'm trying to see if I can calculate *how high* it can go based on how *strong* my flow is through the garden hose, knowing the mass of the toy plane.

The only reason this would occur is that as the contraption rises, it lifts more hose off the ground, consequently becoming heavier -- or the water isn't able to climb up the hoses, and the flow from the nozzles decreases. Otherwise, constant flow from the hoses will cause constant thrust, and the object will accelerate upwards.

 

Similarly, the Harrier has a height ceiling because its thrust decreases with altitude. If the engines kept constant thrust, there would be no limit.

[Klaynos]

Harrier fact of the day.

 

During hover they use more water/second than fuel/second. This is to cool the engine as there the cooling due to air flow is greatly reduced.

[ewmon]

Harrier fact of the day.

 

During hover they use more water/second than fuel/second. This is to cool the engine as there the cooling due to air flow is greatly reduced.

 

Interesting.... the injected water may also produce two other effects: 1) add to the mass of the air flowing through the engine, and 2) increase the thermal efficiency of the engine by using the heat to expand into steam. I suspect that both effects on their own would increase the thrust, resulting in an increase in the engine's static rating, and thus, hover ceiling (although by how much I don't know).

[MigL]

The thrust of the engine will, as long as it is equal to or greater than the weight of the Harrier, sustain a hover at any height according to momentum conservation laws ( or Newton's laws, whichever you prefer ).

 

However the Harrier and aircraft like it have several factors which affect this hover height. It may seem counterintuitive , but hover close to the ground is very difficult. First off you need low jet exhaust velocity or you risk ground erosion. The high speed jet impinges on the ground and causes debris ( chunks of asphalt and concrete ) and hot air to be recirculated into the intakes. Even without the debris, the hot air will appreciably reduce the thrust generated by the Harrier's Pegasus engine. The AV-8B developed from the Harrier used inward angled nozzles and a system of dams to reduce exhaust gas recirculation.

High altitude hover is also very difficult. Again to reduce exhaust velocity which makes the take-offs and landings difficult, most V/STOL aircraft, including the F-35B, use turbofans as opposed to turbojets for their lower exhaust velocity, and don't use reheat ( or afterburning ). Now turbofans produce a lot of their thrust by large, but low compression, fan stages, and as a result loose thrust quickly with altitude. By 40000ft the Pegasus is producing a lot less thrust than it is rated at sea level and probably cannot hover.

 

Aircraft design is a compromise with priorities set by operational requirements. V/STOL aircraft design, even more so as evidenced by the fact that the original Kestrel ( which became the Harrier and AV-8B and could have become the P-1154 ) flew in the late 50s and is only now possibly ( ? ) being replaced by the F-35B.

 

 

[mooeypoo]

The only reason this would occur is that as the contraption rises, it lifts more hose off the ground, consequently becoming heavier -- or the water isn't able to climb up the hoses, and the flow from the nozzles decreases. Otherwise, constant flow from the hoses will cause constant thrust, and the object will accelerate upwards.

 

Similarly, the Harrier has a height ceiling because its thrust decreases with altitude. If the engines kept constant thrust, there would be no limit.

 

.... I completely didn't think abut that, it makes so much more sense now. I don't know why I had this weird idea that the force is diminshed the higher up it goes, as if it is only effective when it "hits" the ground.. that's totally false and against Newton's 3rd law. And yet, I was so confused because I knew the contraption with a model plane will not launch into space, right? it would hover somewhere..

 

Now it makes sense. The weight of the hoses! Ah, I feel like an idiot Seriously, there are rocket launch formulas that involve how a rocket gets *lighter* as it goes up because it loses the weight of the used fuel, and yet in this case with the model plane and hoses, it's exactly the opposite, it "gains" weight the higher it goes!

 

Bah, I feel silly now!

 

Thanks for the answers guys, it helps a lot, and thanks for snapping me back to reality, Capn

 

~mooey

[ewmon]

Okay, mooeypoo, go for it, and we want a SmarterThanThat blog on it complete with your own video

 

Edited May 20, 2012 by ewmon

[mooeypoo]

Omg, I'm so totally doing that...

[doG]

You'll need to take a look at de Laval nozzles and the Venturi effect to account for how the ratio of the nozzles' areas effects the speed and pressure of the exhaust media. In the case of rockets the de Laval nozzle ratios are specifically calculated for the atmospheric pressure at the altitude the rocket engine is designed to operate at. That's why 2nd or 3rd stage engines have a much more pronounced flare than booster engines do.