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Rolling Take offs and Landings

Issue No 47, 9 October 2023

By: Anthony O. Ives

Rolling take offs and landings are considered an advanced operation for helicopters. They are usually neccessary if the helicopter is operating close to its maximum operating weight in a high density altitude (or low air density environment) where there is not enough power to hover before taking off or landing. Rolling landing can also be performed in emergencies such as in the case of a tail rotor pedal becoming stuck at a low power setting. However, this article will look at fixed wing aircraft take offs and landings and mainly the ground run segment, take off and landing do actually have air segment as well.

Helicopters generally perform a rolling take off by accelerating to the translational lift speed [1], which is the speed that helicopters requires the minimum power to operate in steady level flight. They perform a rolling landing by attempting to lift off just above translational lift speed. Fixed wing aircraft accelerate to a rotate velocity noted by V_R this speed is chosen to be above the stall speed and is the minimum speed where the control surfaces are fully effective. V_R is estimated to be about 1.1 V_stall, where V_stall is the stall speed. The take off distance is given by the following equation:

\[s_g = \frac{1}{2 g K_A} ln \left( 1+\frac{K_A}{K_T} V_{R}^2 \right) + NV_{R}\]

Where N is a factor which allows for some extra take off distance it is assumed that N=1 for small aircraft and that N=3 for large aircraft, g is gravity usually assumed to be 9.81 ms^-2. K_T and K_A is defined below:

\[K_T = \frac{T}{W} - \mu_r \]

\[K_A = -\frac{\rho}{2(W/S)} \left[ C_{D0} + \Delta C_{D0} + \left(k_1 + \frac{G}{\pi e A_R} \right) C_L^2 - \mu_r C_L \right) \]

Where T is thrust, μ_r is the runway surface friction coefficient (approximately 0.5 but lower if the runway surface is wet) , W is the aircraft weight (W = mg, m = mass in kg), ρ is the air density, k₁ is an drag factor to take account of lift depend drag as a result of friction and other effects, C_D0 is the zero lift drag, π is the mathematical constant (approximately 3.141593...), e is a wing efficiency factor (you assume 1 if you are not sure what it is), A_R is the wing aspect ratio [2] and C_L is lift coefficient [3].

G is defined a ground effect factor and is given below:

\[G = \frac{(16h/b)^2}{1+(16h/b)^2}\]

Where h is the height of the wing above the ground and b is the wingspan. The ground effect is caused by the wing being close to ground and the trailing vortices are dissapated by the ground reducing the effects of the trailing vortices [4] the same effect can also occur with helicopters hovering close to the ground, in both cases the power required is reduced which will also reduce the ground take off run required.

ΔC_D0 is the drag due to the undercarriage an approximate expression is given below:

\[\Delta C_{D0} = \frac{W}{S} K_{uc} m^{-0.215}\]

Where K_uc is a factor which depends on the amount of flap deflection, K_uc = 5.81 × 10^-5 for a zero flap deflection, K^uc = 3.16 × 10^-5 for a maximum flap deflection.

The K_T is related to the thrust required for take off. The expressions can all be modified to calculate the landing run as well, the landing run is really just the reverse of the take off run. In the case of the landing run the K_T term could refer to reverse thrust in which case the thrust value would be negative. The K_A term is considering the aircraft drag as a more complex form of the drag polar equation, the equations above are based on what I found in number of textbooks [5], [6] and [7]. However, if you do not have all the detailed information required you could just use the simple drag polar equation as below:

\[K_A = -\frac{\rho}{2(W/S)} \left[C_{D0} + k C_L^2 - \mu_r C_L \right) \]

The above expression is much more simplified like most aircraft performance equations the more detail you include the more accurate the answer will be, but you can be surprised by how good an estimate can be got even using the simplest of information. As the aircraft rolls down the runway it is accelerating therefore its speed is increasing which means it lift is increasing which does two things which will effect the take off run required:

The drag will increase mainly due to trailing vortex drag [4]
The friction force will reduce due to the normal reaction reducing

An object resting on a surface produces a normal reaction which is same as the force that is pressing it down on the surface in most cases it is just the weight of the object. If you try to move the object horizontally along the surface you will get force opposing the motion equal to the friction coefficient multiplied by the normal force as given by the expresson below:

\[F = \mu N \]

Where F is the force opposing motion and N is the normal reaction force which is usually equal to the weight of the object, μ is the surface friction. As the aircraft's lift increases the normal force reduces which then reduces the force opposing the aircraft motion. Take off is considered a critcial manuerve an important decision point is usually when the aircraft reaches a speed on the runway before the rotate speed that it does not have enough runway to stop safely. This speed is called V₁, after this speed if the aircraft has emergency and it still has sufficient power and is able to do so it is safer to take off do a circuit and come back in land. Larger helicopters in particular do have similar speeds defined, in some later articles helicopter rolling take offs and landings will be looked at in more detail, they will build upon what was discussed in this article.

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References:

[1] http://www.eiteog.com/EiteogBLOG/No32EiteogBlogForward.html

[2] http://www.eiteog.com/EiteogBLOG/No2EiteogBlogDragCD.html

[3] http://www.eiteog.com/EiteogBLOG/No1EiteogBlogLiftCL.html

[4] http://www.eiteog.com/EiteogBLOG/No35EiteogBlogDrag.html

[5] Aircraft Performance & Design, John D. Anderson Jr., 1999, McGraw Hill

[6] Civil Jet Aircraft Design, Lloyd R. Jenkinson, Paul Simpkin, Darren Rhodes, 1999, Butterworth Heinemann

[7] Aircraft Performance (Cambridge Aerospace Series, Series Number 5), W. Austyn Mair, David L. Birdsall, 1996, Cambridge University Press

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