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I was reading some literature on stalls and spins (which are almost always preceded by a stall) of aircraft when a thought hit me. Why can't a model aircraft (1/4 scale of manned aircraft) be used to inexpensively explore the stall and spin behavior of manned aircraft?

(One disclaimer for this, I know this can't be done at ALL speed ranges or all scales. Airliners are too big to make inexpensive 1/4 scale R/C aircraft, and aircraft that cruise at transsonic speeds will not benefit from this since the effects seen there only happen at that particular reynolds and mach number combination)

However, I was thinking more for aircraft that spend a lot of time at fairly low speed (below Mach 0.3) such as ultralight or light sport aircraft. Here the air is effectively incompressible, meaning flow physics wise, the reynolds number is dominant in determining flow separation. And because of that, all a 1/4 scale model has to do is fly four times faster to get the same flow separation characteristics as the full scale aircraft.

So for an ultralight aircraft, which is speed capped at 30 m/s, a 1/4 scale model would have to fly at 120 m/s to see similar stall behavior, which is at the bottom end of where the flow starts to become compressible, meaning most of the flow structures seen at full scale will be seen at the model scale. Accounting for the lower moment of inertia of the model, the spin behavior of the model should predictably scale to reveal the behavior of the full scale aircraft.

My question is, what am I getting wrong in my reasoning? Why can't this work?

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    $\begingroup$ Spins are "almost" always preceded by a stall? $\endgroup$ – Steve V. Oct 6 '15 at 1:11
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    $\begingroup$ I spun my model aircraft right into the ground the other day :-/ $\endgroup$ – Pugz Oct 6 '15 at 13:17
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    $\begingroup$ Simplest answer; air doesn't scale. An exact scale replica of a larger manned aircraft, with accurate length, width, wing dimensions, mass, CG etc, will still have different airflow characteristics that will skew the results. Despite this, models are often used in wind tunnel testing to determine basic aerodynamic properties; the subtleties, however, must be learned closer to full-scale. $\endgroup$ – KeithS Nov 5 '15 at 21:45
  • $\begingroup$ @SteveV.: A few aircraft have sufficiently high rudder authority that you can enter a flat spin simply by stomping on the rudder and holding it; most post-World War I aircraft have to be stalled to spin, however. $\endgroup$ – Sean Feb 2 at 4:13
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Who says scale models cannot be used for spin modeling?

The key information is that the Reynolds number does not affect the behavior of separated airflow as much, so you do not need to increase speed to compensate for the smaller dimensions. Only when the stall behavior is studied would the Reynolds number matter, but here also meaningful results are possible at lower speeds.

Models are routinely used in spin tunnels. Here both the speed and the dimensions are smaller, but the results can be transferred to the original aircraft. There are two sorts of spin tunnels:

  1. Free tunnels with an open, divergent section in which the model has to be thrown by a skilled operator so it will settle in a spin within the upwards flowing air stream. The section is divergent, so the speed changes with height and allows the model to find a matching speed.

Spin tunnel test in 1959

Picture from spin tests on a Grumman E-2 model in the NACA 20 foot spin tunnel (picture source)

  1. Closed tunnels in which the model is mounted on a sting. The sting is connected to a rotating balance, which can be set at different roll and yaw rates. The resulting matrix of coefficients over angle of attack, angle of sideslip and over the three rotation speeds is fed into a computer model which computes the equilibrium points.

The models used in free tunnels must be scaled both geometrically and inertially, so their mass distribution matches that of the original. If the spin tunnel uses a rotating balance, not even the dynamic scaling of masses and inertias is needed, and a regular tunnel model can be used. However, if the resulting spin is of an oscillating nature, the free spin tunnel is at an advantage, because this becomes readily apparent in the test. In a closed tunnel you just get two equilibrium points and must make the connection yourself.

A third way are free-flight tests of models, but they are much more expensive and allow less observations than wind tunnels.

The stall characteristic is a little harder to predict using models, but again you can draw conclusions from what can be seen in the tunnel. To arrive at the maximum lift coefficient starting from the measured value at Re = 1,000,000, you may use this scaling: $$\Delta c_{L_{max}} = \frac{log_{10}\left(Re^{\frac{1}{6}}\right)}{3.5}$$

The plot below shows the difference in lift coefficient between a small model and a full-scale airplane. The biggest differences are around stall, and at the high angles of attack seen in spins both show fairly similar behavior.

Lift coefficient over angle of attack

Lift coefficient over angle of attack for model and full-scale aircraft, taken from Joseph Chambers' monograph on testing with models (Modeling flight : the role of dynamically scaled free-flight models in support of NASA’s aerospace programs).

For small aircraft, the relative expense of a tunnel test is normally inadequate. Instead, the real thing is used. Since the speeds involved are small, spin tests are carried out with a spin chute or a releasable mass at the tail of the aircraft. On modern designs, even a full-aircraft ballistic parachute system can be employed to prevent a crash if the spin test ends in an unrecoverable situation.

Spin chute installation on a Columbia 400

Spin chute installation on a Columbia 400 (picture source)

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Scaled models are being used to determine spin characteristics of manned aircraft. For example, see this image from Modeling Flight- The Role of Dynamically Scaled Free-Flight Models in Support of NASA’s Aerospace Programs by Joseph R. Chambers:

Spin models

However, there are significant difficulties in correctly modeling the spin characteristics of the aircraft.

For a model to properly simulate a full scale aircraft, both should be dynamically similar- i.e. the flight path and angular displacements of the model and the aircraft will be identical (geometrically)though the timescale will usually vary.

For the model faithfully reproducing the aircraft spin characteristics, the (balance of) aerodynamic and inertial parameters should be similar. The model should be scaled (in addition to the geometrical parameters) in the mass, moment of inertia, linear and angular velocity etc. For example, the scaling factors in case of incompressible flow are:

Incompressible Scale

Image from Modeling Flight- The Role of Dynamically Scaled Free-Flight Models in Support of NASA’s Aerospace Programs by Joseph R. Chambers

In case of compressible flow, still more scaling is required:

Compressible Scaling

Image from Modeling Flight- The Role of Dynamically Scaled Free-Flight Models in Support of NASA’s Aerospace Programs by Joseph R. Chambers

The issue is faithfully duplicating all this scaling is not possible; you are correct that the Reynolds number is the most significant issue involved. Spin involves (partially or fully) separated flows, which are significantly affected by the Reynolds number.

The above mentioned report concludes:

The data show significant increases in the magnitude and angle of attack for maximum lift as Reynolds number increases from model conditions to the full- scale value. Such results can significantly affect the prediction of flight characteristics of the airplane near and above stall.

Another issue is the cost of creating a model; There are significant costs involved in correctly modeling and testing (at-least drop-testing) these systems, the resources for which are not available for all but the most expensive programs. For example, The Spinning of Aircraft- A Discussion of Spin Prediction Techniques, Report no AD- A216- 200 concludes:

The drop-model technique using approximately 1/4 scale-models ... has the potential to cover all phases of the spin. However, because of cost and substantial manpower requirements it only becomes viable for major projects.

These are the reasons we don't see scale models being used to model the spin characteristics of GA and ultralight aircraft.

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  • $\begingroup$ "No, sir, that F-15 isn't ripe yet, you'll have to come back in a year or two to pick it." $\endgroup$ – Sean Feb 2 at 4:15

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