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Gliding Flight

Issue No 42, 4 September 2023

By: Anthony O. Ives

The thing I most like about gliders is that they are one of simplest aerodynamic flying machines you can make using wood, of course you could say a paraglider is simpler but building one seems more complex to me. Gliders rely on their very efficient aerodynamics and enviromental updrafts to stay airborne for as long as possible. The equations to calculate a glider's performance are also quite simple and can be easily derived from the equilbrium of all the forces acting on the glider. However, the gliding performance of a fixed wing powered aircraft can also be important as in the case of engine failure the aircraft should be able to glide safely back down to the surface.

I only had a very short lived experience with full size gliders consisting of two very short flights however, I did fly radio controlled (RC) gliders a bit more, they were probably the only fixed wing RC aircraft I enjoyed flying before I started flying RC helicopters and then full sized helicopters. In the case of the RC gliders that I flew they had an electric motor, so you use the motor to get the glider to certain height and then try to find some rising air currents to keep the glider in the air for as long as possible. Full size gliders can use a tow plane or a winch system to get the glider to the launch height.

If the glider pilot cannot find any rising air then the glider will have a gliding flight range according to the following equation:

\[R_{max}=h \left(\frac{L}{D}\right)_{max} \]

Where h is the launch altitude, L is the lift, D is drag and R_max is the maximum range. The lift and drag should be in the same units usually Newtons and the launch altitude and the maximum range should also be in the same units usually feet or metres. The equation for minimum glide angle is as following:

\[\frac{1}{tan(\theta_{min})}=\left(\frac{L}{D}\right)_{max}=\frac{R_{max}}{h} \]

Where θ_min is the minimum glide angle, these equations will give the maximum range and the minimum glide angle if the lift to drag ratio is a maximum. The equations basically tell you the higher the lift to drag ratio the further the glider can travel. In the case of an engine powered aircraft suffering an engine failure the launch altitude would become the altitude at which the engine failure occurs.

However, if you are interested in the maximum amount of the time the aircraft can stay up then the following equation for gliding flight endurance is:

\[E=\frac{h}{v_{descent(min)}}\]

Where: \[v_{descent(min)}=\sqrt{\frac{2}{\rho} \frac{W}{S} \frac{1}{C_L^{3/2}/C_D}}\]

Where E is the endurance, v_descent(min) is the minimum rate of descent, W is weight, S is wing area, C_L is lift coefficient and C_D is drag coefficient. Essentially the glider will stay up the longest when \(C_L^{3/2}/C_D\) is at its maximum. Usually glider pilots win competitions based on the maximum range they can achieve but the equations for v_descent(min) may be of interest to them as this will be the minimum amount updraft they will need to maintain their altitude and if they can find rising air exceeding this value they can use it to climb to a higher altitude which as you seen for the equation for maximum range, a higher altitude means more range.

In a later article we will discuss ratios \(C_L^{3/2}/C_D\) and L/D (which is same as \(C_L/C_D\)) but by varying the airspeed of the glider the pilot can choose which ratio is the maximum hence whether he is flying for maximum range with no drafts or whether they want to maintain their altitude or climb to a higher altitude. Of course the pilot of a conventional fixed wing powered aircraft can use a similar technique to plan a safe landing in the event of an engine failure. It also worth noting the maximum aerodynamic ratios which give maximum gliding range and endurance are the same as those for the propeller powered aircraft [1],[2] but different for jet powered aircraft [3].

Gliding performance is not relevant to helicopters though it may be relevant to other VTOL aircraft with fixed wings such as tiltrotors, though it does explain one of the reasons why some people suggest helicopters are more survivable in an engine failure scenario. For fixed wing aircraft to stay airborne including when it is gliding it must have some forward speed, hence why a fixed wing aircraft needs a runway to land safely. The trouble with engine failures is that they can happen anywhere and given the forward momentum a fixed wing aircraft will at least be damaged in forced landing if it cannot find a wide open area with a smooth surface. In the case of a helicopter engine failure this is less of a problem as they can be landed with no or very little forward momentum which means it is more possible to carry out a forced landing of helicopter with no damage.

Apart from a general aerodynamic theory view point gliding flight is really irrelevant to helicopters however, in some later articles I may use the gliding equations to compare gliding flight of some fixed wing aircraft with helicopter autorotation flight. There could also be some practical gliders that could be used to assist with navigation or seach and rescue operations. The Zephyr [4] is one project which I know that is looking at the feasibiliy of replacing satelites with unmanned solar powered gliders. The Zephyr which is described by airbus as follows 'The high-altitude pseudo-satellite (HAPS) is the first unmanned aircraft of its kind to fly in the stratosphere. Capable of flying for months at a time, it combines the endurance of a satellite with the flexibility of a UAV.'

Using the equations for gliding range and endurance as well as the aircraft specifications and dimensions calculated in references [1], [2] and [5] to [8] you could calculate the gliding range and endurance at different altitudes for the design looked at in those articles. Let me know via comments or email how you get on or if you have any problems. More information on general aircraft performance including further information on the aerodynamic ratios can also be found in References [9] to [11].

Please leave a comment on my facebook page or via email and let me know if you found this blog article useful and if you would like to see more on this topic. Most of my blog articles are on:

Mathematics
Helicopters
Woodworking and Boatbuilding

If there is one or more of these topics that you are specifically interested in please also let me know in your comments this will help me to write blog articles that are more helpful.

References:

[1] http://www.eiteog.com/EiteogBLOG/No6EiteogBlogRange.html

[2] http://www.eiteog.com/EiteogBLOG/No7EiteogBlogEndurance.html

[3] http://www.eiteog.com/EiteogBLOG/No41EiteogBlogJet.html

[4] https://www.airbus.com/en/products-services/defence/uas/uas-solutions/zephyr

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

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

[7] http://www.eiteog.com/EiteogBLOG/No3EiteogBlogMass.html

[8] http://www.eiteog.com/EiteogBLOG/No4EiteogBlogThrust.html

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

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

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

Disclaimer: Eiteog makes every effort to provide information which is as accurate as possible. Eiteog will not be responsible for any liability, loss or risk incurred as a result of the use and application of information on its website or in its products. None of the information on Eiteog's website or in its products supersedes any information contained in documents or procedures issued by relevant aviation authorities, manufacturers, flight schools or the operators of aircraft, UAVs.