How much farther will more aerodynamic object fly at higher speeds

[kokes]

Hi,

I invented a new type of arrow stabilizer. It is an aerodynamic turbine that makes the arrow to be stabilized by rotation mainly. In my field tests I reach 15% increase in distance compared to standard fletched arrow. My bow is very weak, it consists of a bent bamboo stick and a string. The speed of my arrow is therefore very slow, i estimate 100 kmh^-1.

Now I am wondering what happens if I increase the speed. What happens if I mount the same stabilizer to an airplane flying 1000 kmh^-1 instead of its rear stabilizers? Even more extreme case would be a rocket. It has the same overall shape as an arrow, uses same type of stabilization, but it flies much faster, say 40 000 kmh^-1. How much fuel would this save?

I read air drag increases with square of speed, but I am not sure how to estimate the distance increase resulting from more aerodynamic stabilization (which gets my arrow 15% further at 100 kmh^-1).

It is more tricky than that since not only does the arrow fly further, it also flies faster, which makes this whole question much more complicated. But let's say it flies just as fast, say I don't put the pedal all the way to the metal.

What I figured was:
Well, the rocket flies 400 times faster. That means that the difference would be 1.15^400. But that means it would fly 1,901,674,318,152,855,051,262,401 times further, which makes no sense.

Can anyone help? What am I doing wrong? Can an airplane or a rocket benefit from this at all?

Thanks a lot.

Jan Kokes

PS: Version 1 of my turbine 3D model can be downloaded from here, there are some pics there etc.
PPS: The patent of version 1 is expired, you are wellcome to experiment if you wish.

 

[A.T.]

It is an aerodynamic turbine that makes the arrow to be stabilized by rotation mainly.
...

What happens if I mount the same stabilizer to an airplane flying 1000 kmh^-1 instead of its rear stabilizers?

The passengers would not be happy

Even more extreme case would be a rocket.

Unguided rockets already use stabilization though rotation, created by fins, rifled nozzles or nozzle fins. Some guided missiles rotate too:
http://en.wikipedia.org/wiki/RIM-116_Rolling_Airframe_Missile

 

[billy_joule]

I looks like your arrow design has a greater projected area than regular arrows in which case generally you'd expect more drag. I suspect there are other factors at play here.

For rockets, I would guess your design would give far greater rotational force than was required for stability.

Fins with very small projected area can give rockets sufficient spin (and be easily controlled), why replace them with something with more drag?

 

[kokes]

The passengers would not be happy

Unguided rockets already use stabilization though rotation, created by fins, rifled nozzles or nozzle fins. Some guided missiles rotate too:
http://en.wikipedia.org/wiki/RIM-116_Rolling_Airframe_Missile

Thank you for your reply. I am aware of both points. I can solve the former by counterspin using second turbine with opposite spin. They can both be braked indepently and operated by computer to keep passanger area free of spin. I think fuel reduction would easily pay for added expences.

Yes, the spinning missles have been around at least since 50s. They use drag powered turbines, which is completely different issue. I use lift powered turbine, which "runs away" from the drag. My observation concerning distance and precision of arrows is:

- Arrow with no stabilization flies furthest (70 steps), but it flies weirdly and lands somewhere in general direction of the shot.

- My spinning arrow flies almost as far as arrow with no stabilization (66 steps), it's trajectory is very predictable.

- Regular arrow flies shorter distance than my arrow(55 steps), it's trajectory is quite predictable, but it fishtails a lot.

- Spinning arrow with screwed fletches flies shortest distance (50 steps), it's trajectory is very predictible.

The steps are mean value of my trial shots. Measuring in steps is not the most precise way of doing it, but it is very convenient for me. Notice the distances are very short, ordinary bow can shoot about 250 meters, record shot being about 2 kms.

 

[kokes]

I looks like your arrow design has a greater projected area than regular arrows in which case generally you'd expect more drag. I suspect there are other factors at play here.

For rockets, I would guess your design would give far greater rotational force than was required for stability.

Fins with very small projected area can give rockets sufficient spin (and be easily controlled), why replace them with something with more drag?

I made some pictures of my recent arrow. The surface area of fins is about 7 times smaller than that of original arrow. My blade is much smaller, it has opening in it and there is just one instead of 3. Frontal area is hard to tell, but it is also smaller than area of 3 blades at original arrow.

I am trying to make the turbine as small as possible and see if it is still sufficient for rotating. Right now I am limited by my skills. The (master) turbines are hand made, the 3D printers I know about are all useless for something so small.

My arrow is more aerodynamic and create less drag than fins, that is the whole point. It uses air flowing around the turbine blade to create lift instead of letting the air hit the turbine to create drag. The blade actually avoids the incomming air. That is why it is twisted. It may look almost the same as drag turbine, but it is a totally different principle, much more efficient one.

 

[A.T.]

I can solve the former by counterspin using second turbine with opposite spin.

Then you don't have any stabilizing effect, because the net angular momentum is zero.

I think fuel reduction would easily pay for added expences.

Planes already have enough aerodynamic control surfaces to stabilize them. They don't suffer from avoidable drag because of wrong alignment to the flow like an unstable arrow, because they have the optimal alignment in cruise flight. Adding turbines will increase fuel consumption, and offer no gains at all.

Yes, the spinning missles have been around at least since 50s. They use drag powered turbines, which is completely different issue. I use lift powered turbine, which "runs away" from the drag.

All turbines with an axis aligned with the flow are lift powered.

 

[kokes]

Hi A.T., thank you for your response. I am affraid this time I disagree with most of the things you wrote. Please correct me if I am wrong:

Then you don't have any stabilizing effect, because the net angular momentum is zero.

I disagree. The momentum of both turbines and everything that spins along with them will have stabilizing effect regardless of direction of their spin. Look at marine gyroscopes. The ship itself doesn't spin, the gyroscopes don't spin in one direction, but the ship is stabilized.

Planes already have enough aerodynamic control surfaces to stabilize them. They don't suffer from avoidable drag because of wrong alignment to the flow like an unstable arrow, because they have the optimal alignment in cruise flight. Adding turbines will increase fuel consumption, and offer no gains at all.

I disagree partially. The planes do have enough aerodynamic control surfaces to stabilize them. But if they used rotation instead of plain drag stabilization they could diminish their overall drag provided rotation is created in a way that uses less drag, ie by a (very good) lift powered turbine.

All turbines with an axis aligned with the flow are lift powered.

I disagree completely. All turbines with an axis aligned with the flow are horizontal axis turbines. Look at american windmill or Parsons turbine. They are both horizontal and drag powered. As a matter of fact the lift powered horizontal turbine design is very rare. So far there has been the one that looks like an airplane propeller, plus various minor modifications thereof. Another one is the one used by Starrflight FOBs. And another one is the one I designed. That's all.

 

[A.T.]

I disagree. The momentum of both turbines and everything that spins along with them will have stabilizing effect regardless of direction of their spin.

Angular momentum is a vector. For two coaxial turbines with the same but opposite angular momenta, the total angular momentum is zero, so there is no gyroscopic stability of the axis.

...instead of plain drag stabilization... drag powered...

You either don't understand how lift and drag are defined, or are using some non standard definition. Please define the following terms formally, as you understand them: drag, lift, drag stabilization, drag powered.

 

[kokes]

Angular momentum is a vector. For two coaxial turbines with the same but opposite angular momenta, the total angular momentum is zero, so there is no gyroscopic stability of the axis.

You were right. I just searched this very forum and found the answers. In order to achieve the stabilization one turbine will have to be heavy and the other light, latter being in place just for the angular velocity to cancel out the spin. Or electric motors could be used as is the case in satellites. Thank you for expending my knowledge.

You either don't understand how lift and drag are defined, or are using some non standard definition. Please define the following terms formally, as you understand them: drag, lift, drag stabilization, drag powered.

Lift force is created by higher speed of flow created by a narrow passage on one side of the blade, which acts like a wing of an airplane. Higher flow speed results in lower pressure (Bernoulli), which sucks the blade toward it (the blade is pulled).

Drag force is created by air hitting the blade and pushing it from the way (the blade is pushed).

Drag stabliziation is the one used i.e. by ordinary arrow. Rear of the arrow is less aerodynamic because of higher drag, it lags behind and thus keeps the arrow flying straight.

By drag powered I mean it (turbine) is spun by fluid hitting its blades and moving them away in a process, making it spin.

 

[A.T.]

Lift force is created by higher speed of flow created by a narrow passage on one side of the blade, which acts like a wing of an airplane. Higher flow speed results in lower pressure (Bernoulli), which sucks the blade toward it (the blade is pulled).

Drag force is created by air hitting the blade and pushing it from the way (the blade is pushed).

This aren't formal definitions but informal explanations. The common formal definitions are:

Lift : Fluid-dynamic force component perpendicular to the relative flow
Drag: Fluid-dynamic force component parallel to the relative flow

Given these definitions its obvious that any turbine with an axis parallel to the flow, is being turned by the lift component of the force at the blades. The drag component creates no torque or a torque opposed to rotation.

Planes and arrows are also mainly stabilized by the lift component of their fins.

 

[kokes]

Ok, I understand what you mean. Given these definitions you are right. In turbines, however, lift and drag power refer to what I described. Pull vs. push.

Let me rephrase myself, so it is all clear now:

There are two ways flying object can be stabilized. Either by drag stabilization (rear lagging) or by rotation.

Vertical (tangential to flow, Lift in your dictionary) turbines would require transmission, plus their efficiency is lower than in horizontal (parallel to flow, Drag in your dictionary) turbines.

Out of thousands of horizontal (parallel to the flow) turbines, vast majority of them are drag (push) powered, few are lift (pull) powered. The drag (push) turbines have been tested for over 500 years and they take away too much energy from the arrow (ship, sub, airplane, airship, missle, rocket...). One of the lift turbines (propeller type) is inefficient in high speeds and bad from structural point of view (extenrnalities break off). Second one is unkown (guys from Starrfligh never answered my enquiries), most likely less efficient, third one is more efficient in stabilization than plain drag stabilization.

Now, just for fun, let's make this even more confusing:

My turbine is lift (pull) powered, but it can also be drag (push) powered if I twist the blades more so that they don't run away from the incomming air fast enough and get hit by it. In that case the turbine becomes lift-drag combined turbine. Concerning positioning, I use my turbine as horizontal (parallel), but due to its egg based shape (similar shape from side as well from the top) it is also vertical (tangential) at the same time. As a vertical (tangential), however, it is only powered by drag (push), not by lift (pull).

 

[A.T.]

In turbines, however, lift and drag power refer to what I described.

Can you provide references for your alternative definitions of lift and drag, which are precise and quantitative, not just descriptive? Without them your statements are meaningless.

 

[kokes]

Drag Design
Blade designs operate on either the principle of drag or lift. For the drag design, the wind literally pushes the blades out of the way. Drag powered wind turbines are characterized by slower rotational speeds and high torque capabilities. They are useful for the pumping, sawing or grinding work that Dutch, farm and similar “work-horse” windmills perform. For example, a farm-type windmill must develop high torque at start-up in order to pump, or lift, water from a deep well.

Lift Design
The lift blade design employs the same principle that enables airplanes, kites and birds to fly. The blade is essentially an airfoil, or wing. When air flows past the blade, a wind speed and pressure differential is created between the upper and lower blade surfaces. The pressure at the lower surface is greater and thus acts to “lift” the blade. When blades are attached to a central axis, like a wind turbine rotor, the lift is translated into rotational motion. Lift-powered wind turbines have much higher rotational speeds than drag types and therefore well suited for electricity generation.

- See more at: http://www.iowaenergycenter.org/wind-energy-manual/wind-energy-systems/#sthash.DoKOscYS.dpuf

 

[A.T.]

Drag Design
Blade designs operate on either the principle of drag or lift. For the drag design, the wind literally pushes the blades out of the way. Drag powered wind turbines are characterized by slower rotational speeds and high torque capabilities. They are useful for the pumping, sawing or grinding work that Dutch, farm and similar “work-horse” windmills perform. For example, a farm-type windmill must develop high torque at start-up in order to pump, or lift, water from a deep well.

Lift Design
The lift blade design employs the same principle that enables airplanes, kites and birds to fly. The blade is essentially an airfoil, or wing. When air flows past the blade, a wind speed and pressure differential is created between the upper and lower blade surfaces. The pressure at the lower surface is greater and thus acts to “lift” the blade. When blades are attached to a central axis, like a wind turbine rotor, the lift is translated into rotational motion. Lift-powered wind turbines have much higher rotational speeds than drag types and therefore well suited for electricity generation.

- See more at: http://www.iowaenergycenter.org/wind-energy-manual/wind-energy-systems/#sthash.DoKOscYS.dpuf

This is just more vague descriptive handwaving targeted at laymen. No quantitative defintion of terms or distinction of the two types, except that one design spins slower. Things like pressure difference, lift & drag exist in slow moving farm-type windmill as well, so that is not a distinction.

Also, even by this description, your claim that planes use drag for stabilization is nonsense. The lift/drag ratio of the fins in normal flight is comparable to the wings. The correcting torque is created mainly by their lift.

 

[kokes]

What I meant was the rear tail. This is what creates drag (or air resistance) I was referring to:

This can be replaced by something much smaller but equally functional, reducing overall air resistance, saving unknown amount of fuel. How much the unknown amount is is what I would love to find out.

 

[cjl]

What I meant was the rear tail. This is what creates drag (or air resistance) I was referring to:

View attachment 73079

This can be replaced by something much smaller but equally functional, reducing overall air resistance, saving unknown amount of fuel. How much the unknown amount is is what I would love to find out.

You have not shown that it can be replaced by something lower drag, and in fact, your proposal sounds like it would greatly increase drag. A windmilling propeller is extremely high drag. This is one of the reasons multi-engine propeller aircraft must be able to feather the propeller on an engine if they experience an engine failure. The drag from a propeller driven by the freestream is so high that the airplane might be unable to stay in the air if it could not feather (and stop) the prop.

An airfoil at near zero angle of attack on the other hand (such as the vertical stabilizer pictured) is very low drag.

I'm similarly skeptical of your methodology and results with the amateur rocket example - inducing spin with a rocket's fins tends to decrease performance (the energy to spin the rocket has to come from somewhere, and it comes out of the forward velocity), but it is usually done with things like sounding rockets because it decreases the trajectory dispersion, and also keeps the rocket stabilized after it has reached an altitude at which aerodynamic stabilization is no longer possible. If maximum performance is desired though, spin is detrimental.

 

[kokes]

Never mind then, I will stick to my arrows and work my way up. Real life experiments will tell. I didn't come to argue. I have one question and no one even tried to answer, except for myself.
Jan

(Otherwise my response would have been something like: I mentioned twice that drag powered turbines have been tested and they don't work... 16th century crossbows... Yes, jet engine turbine won't work... Drag powered... Two ways to stabilize... Not proven that rotation must be more energy intensive... And so on.)

 

[cjl]

I'm sorry if that wasn't the response you wanted, but the fact is that aerodynamics are fairly well understood, and it's very unlikely that you will come up with something revolutionary through this kind of experimentation (especially with how many billions of dollars are spent trying to improve aircraft efficiency). As for your parenthetical bit, I can't really parse any of that, and I still don't know why you keep talking about "drag powered" turbines and jets.

 

[duri]

Kokes, you are trying some very old concept. Spin stabilization would not decrease the drag but it will increase. Higher range you got is not due to lower drag. But it is a consequence of better stability. Try this one for understanding how stability contributes to range for uncontrolled and no powered flight. Add some dead weight to the arrow near the nose cone and find the range. Do the same by moving the weight to some next downstream location along the arrow. You would find, at some location of dead weight range would be maximum. This has nothing to do with drag.

 

[kokes]

I'm sorry if that wasn't the response you wanted, but the fact is that aerodynamics are fairly well understood, and it's very unlikely that you will come up with something revolutionary through this kind of experimentation (especially with how many billions of dollars are spent trying to improve aircraft efficiency). As for your parenthetical bit, I can't really parse any of that, and I still don't know why you keep talking about "drag powered" turbines and jets.

I am back. No problem, I am not upset at all. I now fairly well understand how my arrow works, I will keep that for a separate post. Let me reply first:

Billions of dollars spent mean nothing if no significant discovery comes out the other side.

Regarding jet engines. I like those a lot. There are two types of turbines there. But first thing first. Horizontal axis drag powered (push) turbine and ventillator are pretty much the same thing. They look the same and can be used one in place of the other. The difference is how it is used. Turbine consumes flow and turns it into rotation, while ventilator does exactly the opposite, it consumes rotation and turns it into flow.

The two turbines in the jet engine are:
- compressor
- turbine

The jet compressor consists of multiple stages of ventillators. And ventillators are turbines. That's why I talked about drag powered (push) turbine in jet engines.

Aside from that the jet turbine itself is also drag powred (push) horizontal turbine.

 

[kokes]

Arrow principle

This post may seem strange at first. Let me start it off with some results:

My arrow now flies more than twice as far as original arrow with fletches. It also flies significantly further than arrow with no stabilization, which should be the most aerodynamic one of them all.

This seem to defy laws of physics. It doesn't. Let me explain.

My arrow is quite complex machine. It doesn't look it, but it has many function built into its design. The most important functionalities of my arrow are:

- it is a stabilizer
- it is a turbine
- it is a propeller.

Most importantly, it is all of the above at the same time.

When I shoot my arrow, it consumes part of its energy and turns it into rotation (turbine). The rotation is used for stabilization (stabilizer). At the beginning the arrow flies very fast, so the turbine starts spinning very fast too. But the arrow slows down. When the forward speed diminishes enough, the spinning speed is too high and the turbine stars working as a propeller. It pushes air to the rear and speeds the arrow up. Rotation decreases, forward speed increases. That is going on until the forward speed surpasses the rotation speed. Then the arrow starts slowing down again. And so on and so forth.

So my arrow is actually a complex machine. It harvests kinetic energy and transfers it into a rotation. It uses rotation to stabilize itself and to store excess energy. When the arrow slows down it transfers the energy of rotation into increased speed.

Ordinary arrow doesn't recycle the excess energy for stabilization. It is gone forever. Unstabilized arrow may be more aerodynamic than mine, but the same thing applies. It doesn't transfer, store and reuse its energy.

 

[kokes]

Kokes, you are trying some very old concept. Spin stabilization would not decrease the drag but it will increase. Higher range you got is not due to lower drag. But it is a consequence of better stability. Try this one for understanding how stability contributes to range for uncontrolled and no powered flight. Add some dead weight to the arrow near the nose cone and find the range. Do the same by moving the weight to some next downstream location along the arrow. You would find, at some location of dead weight range would be maximum. This has nothing to do with drag.

Thank you for your reply. Very interesting point. I agree with most. I have even done similar tests before.

 

[pbuk]

Like one of these? I had one for a while, it was great fun until the dog ate it.

 

[A.T.]

That's why I talked about drag powered (push) turbine in jet engines.

Aside from that the jet turbine itself is also drag powred (push) horizontal turbine.

As long as you don't define "drag powered" in precise quantitative terms, it's just meaningless gibberish.

 

[A.T.]

- it is a turbine
- it is a propeller.

Most importantly, it is all of the above at the same time.

It can't be a turbine and propeller at the same time. It either roates with the net aerodynamic torque on it (turbine) or against it (propeller).

At the beginning the arrow flies very fast, so the turbine starts spinning very fast too. But the arrow slows down. When the forward speed diminishes enough, the spinning speed is too high and the turbine stars working as a propeller. It pushes air to the rear and speeds the arrow up. Rotation decreases, forward speed increases.

Converting linear speed into rotation and then back into linear speed is a lossy process, so there is no net gain from it.

 

[cjl]

Converting linear speed into rotation and then back into linear speed is a lossy process, so there is no net gain from it.

This is true, but it is actually possible that an arrow could fly farther in this case, due to the way an arrow gains energy (all in one lump sum right at the beginning). Because drag force has a v² relationship with velocity, the energy lost by an arrow in flight over a given distance will also be proportional to v². If you convert a substantial proportion of translational kinetic energy into rotational kinetic energy right at the beginning, it will slow down the arrow, and thus the drag losses will be lower. Therefore, with the same amount of starting energy, it could end up with more energy in the end due to lower losses (because this in effect causes the arrow to gain kinetic energy throughout the flight from the stored rotational energy). To put it another way, for a given amount of energy, an object will fly farther if you distribute the kinetic energy addition throughout the flight rather than giving it one giant push at the beginning.

That effect would not work on an airplane though. The lower losses (assuming the arrow works at all) are only because the arrow is flying slower. With an airplane, to take advantage of this, you would just have to design it with a lower cruise speed. The drag coefficient of this design is definitely higher than for a standard arrow, so if you hold cruise speed constant for an airplane, there is no benefit. Airplanes already distribute the kinetic energy addition, since they are storing the energy in the form of fuel.

 

[A.T.]

To put it another way, for a given amount of energy, an object will fly farther if you distribute the kinetic energy addition throughout the flight rather than giving it one giant push at the beginning.

1) You are forgetting gravity here. If you slow down the arrow to spin it, gravity will bring it down quickly. If you use the rational energy to counter gravity, you are wasting it without gaining distance. And the more you have slowed down the arrow initially, the more time it will need to cover distance, and the more energy per distance you waste to counter gravity .

2) Even without gravity, I doubt this scheme could increase distance in practice, without a variable pitch rotor or a gearbox between the rotor and the rotating mass. An arrow has neither. Maybe you could get a slight improvement for an object that has extremely high drag even without the rotor. But I doubt for an arrow.

 

[cjl]

I think the importance of gravity depends a lot on the amount of energy we're talking about here. That having been said, I do agree that in practice, I would be very surprised if this was actually effective. I do at least see some ways in principle that it could kind of work though.

 

[A.T.]

I think the importance of gravity depends a lot on the amount of energy we're talking about here.

Every bit of energy you convert into rotation increases the flight time and gives gravity more time to pull the arrow down. I doubt the reduction in drag can compensate for that. How big is the initial drag of the arrow (without the blades) compared to the gravitational force on it?

And those fixed pitch blades almost never operate at optimal L/D ratio. So the double conversion of linear KE -> rotational KE -> linear KE will be highly inefficient in practice.