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I have read numerous books and researches, but I couldn’t find any formulae that actually work for how to calculate the following (for commercial aircrafts):

1- Drag coefficient for a retractable landing gear.

I tried the following equations:

CD,gear = WingLoading * FlapDeflection * (( AircraftMass(TO,LD))^-0.215)

CD0,gear = SUM i=1 > n [CD,gear(AreaLG / WingArea)]

The results were ASTRONOMICAL

2- Weight of main and nose landing gears.

LG weights are calculated as a percentage of the MTOW, but different sources had different percentages (Normally between 3.8% and 6%). That doesn’t really seem to be the case; For example, a Boeing 747–400BCF’s MTOW is 410 tonnes. Based on my research, the wing-mounted gears (2) are 2952 kg EACH, body-mounted gears (2) are 2924 kg EACH, and the nose gear is 1432 kg. In total, main landing gears weigh 11752 kgs, which is, roughly, 2.9%. If the nose landing gear weight is added to the calculation that’d be 13184, which is 3.2% for ALL landing gears combined!

If anyone knows how to calculate the CD or weights, please help. Very much appreciated!

Cheers

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    $\begingroup$ How did you decide that the drag coefficient of the landing gear would vary based on Wing loading or flap deflection or aircraft mass? Cd basically says how much force is exerted on the gear as the aircraft moves through the air (well, when multiplied by 1/2 rho V squared times the frontal area of the gear). Similar to when you stick your hand out the window of a moving car and then either hold your hand palm down or palm forward you are changing the drag coefficient of your hand. But that CD of your hand has nothing to do with how much the car weighs or whether the trunk is open. $\endgroup$
    – Jim
    Commented Dec 24, 2022 at 0:53
  • $\begingroup$ I understand that. You are absolutely correct! That's why I said I couldn't find anything that actually works or makes sense. The formulae stated in the question were found in "Drag Force and Drag Coefficient: Chapter 3." It doesn't make sense, hence why the results were astronomical. $\endgroup$
    – John Howell
    Commented Dec 24, 2022 at 0:53

2 Answers 2

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1. C$_D$

This data might be in the aeroplane design books in statistical form. A quick look in the one I have, Synthesis Of Subsonic Airplane Design by E. Torenbeek, has some data for slow, fixed wing aeroplanes in Appendix F.

Fluid-Dynamic Drag from Sighard Hoerner states the following on page 13-15:

Retractable Landing Gears (it seems) are often designed without much care for the aerodynamic shape in the extended position. The drag coefficient (based on wheel area) is in the order of $C_{D◻︎}$ == 0.6 or 0.8....for configurations with cylindrical struts.

The emphasis on Wheel Area in above citation is mine, the value would have to be converted to the wing area reference $C_D$.

enter image description here

A further source was found in my paper copy handout of Airplane Performance, VTH-D 14 by Prof. Wittenberg, for a Convair 240. The increase in $C_D$ is relatively constant over the $C_L$ range, about 0.02.

2. Weight This one is in Torenbeek, page 280 gives an overview for several jet transports, relevant data 35 years ago but still giving a good general trend.

enter image description here

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No idea which sources you are referencing, please be specific when referring to a reference.

You should check out Curry's book on landing gear design.

There is also an extensive report put together by one of Bill Mason's grad students.

Curry doesn't do a whole lot for drag, but it has a nice section on conceptual design level weights (Ch. 11) as well as more detailed treatment in the rest of the chapters.

His data shows that the total weight of all landing gear (main and nose) is about 3.5 to 4% of max landing weight (slightly less of max gross). This is true across a wide swath of aircraft types. He provides modifiers for longer/shorter gear and rough field requirements, etc.

Landing gear can be a huge contributor to an aircraft's drag. Gear accounted for half the drag of a clean flying wing radio controlled aircraft I designed once. The wheels and struts all likely have separated flow -- which is very draggy.

Use Hoerner and build up a drag estimate based on cylinders for the struts and the given data on wheels. It isn't too complex

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