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I plan to have dragons in my fantasy setting and wanted to figure out just how much force their wings would need to generate in order for them to fly.

Rules for dragons in this setting:

  • Dragons, and other large flying creatures have stronger bones, muscles and skin to enable them to fly granted to them by a wide variety of conditions that varies from species to species.
  • The only magic dragons have naturally is their breath attacks in some dragon species. They do not use magic to fly.
  • While dragons are capable of flight from a young age, adult dragons are not very agile in the air and prefer to fight on the ground. Younger dragons will have agility that diminishes as they grow.
  • We'll be setting aside the usual problems of the square cube law for things like heat regulation and metabolism since this is a fantasy setting.

I'm just looking at the amount of force their wings would need to produce in order to fly so that I can determine how much force they could exert if they tried to flap their wings to create a directed air blast to topple foes and possibly weak buildings.

Image Source: D&D Monster manual (3rd edition)

Image Source: D&D Monster manual (3rd edition)

For reference, this is what I was considering for a full grown dragon in my setting at least in terms of body plan and proportions. Without any measurements of the reference image, I'm going to fall back on what one of the D&D books describe for a large dragon. 2700 pounds and a 45-50 foot wingspan will be the average.

With all of that out of the way, how much force would a dragon of about that weight and wingspan need to fly? And how much of it could they direct in front of them as an attack? Would it topple humanoid foes or just kill them? Could it wreck some buildings and fortifications?

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    $\begingroup$ The dragon in your illustration looks a bit pre-Lilienthal, in terms of wing span.. and yes, it could inflict relevant damage when it falls down on your toes. Dropping this dragon at say, 400 feet altitude, it will definitely fall through most roofs. $\endgroup$
    – Goodies
    May 1, 2022 at 22:41
  • $\begingroup$ Off the topic. Flying creatures have hollow bones they can't weigh that much. The largest flying creature weighed around 550lb with10meter wingspan. To have that much weight your dragon needs to be way bigger relative to the human in the image. $\endgroup$
    – the Hutt
    May 2, 2022 at 6:50
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    $\begingroup$ Not an answer, but consider ability to blind foes! Even if the gust really is not that strong, forcing opponents to cover their eyes (or actually blinding them) can give a dragon an opening to chomp/burn/claw. $\endgroup$
    – PipperChip
    May 2, 2022 at 14:37
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    $\begingroup$ You might want to 1) be more flexible with the wingspan and 2) add the science-based tag to your question. $\endgroup$
    – Mindwin Remember Monica
    May 2, 2022 at 15:42
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    $\begingroup$ Please credit the image source and copyright info, else you risk the image being taken down. $\endgroup$
    – Escaped dental patient.
    May 3, 2022 at 1:59

4 Answers 4

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In theory if we knew the dragon's wing area, coefficient of lift, coefficient of drag, and dragon's maximum flight speed, we could determine their thrust. However we don't know your dragon's max flight speed, Cl, or Cd.

In level flight Lift = Weight and Lift/Drag = Weight/Thrust. If we know the lift drag and weight we could then easily determine thrust. Determining lift and drag is non-trivial. Given the many unknown quantities deriving thrust this way is a bit of a dead end.

For completeness:

The equation for lift is L = (1/2) * d * v^2 * s * Cl where:

  • L is lift
  • d is the density of the air
  • v is the velocity
  • s is the area of the wing
  • Cl is the coefficient of lift

The equation for Drag is D = (1/2) * d * v^2 * Cd * A where:

  • D is drag
  • d is the density of the air
  • v is the velocity
  • Cd is the coefficient of drag
  • A is the reference area

However if we assume that your dragon can hover we can derive some numbers that don't rely on as many undefined quantities. Unlike level flight where aerodynamic lift counteracts the force of gravity, downward thrust needs to counteract gravity on it's own. This greatly simplifies the equations.

For a 2700 pound (1225 kg) dragon to hover it needs overcome the force of gravity, without the help of aerodynamic lift. At a minimum it will need to be able to produce at least 2700 pounds of force (about 12000 Newtons). Add an extra 25% to that to give your dragon some ability to climb and you're looking at a total thrust of 15000 N. Given that in level flight migratory birds like geese have thrust to weight ratios as low as 0.05 having a TWR of 1.25 should make your dragon a quite capable and aerobatic flyer.

To put that thrust in perspective that's slightly less thrust than the Messerschmitt Me 262's two engines combined. While your dragons still put out a lot of thrust, unlike a jet engine where the thrust is concentrated in one location, that power is going to be dispersed over the full area of the 50ft (15m) wingspan.

Getting caught in the downwash of your dragon's wings is going to be noticeable but isn't going to do any structural damage.

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    $\begingroup$ Keep in mind that a dragons wings are only going to provide this much lift on average, and will presumably produce less lift (if any) on the upstroke as compared to the downstroke. With this in mind you can probably double that figure. $\endgroup$
    – Turksarama
    May 2, 2022 at 3:18
  • $\begingroup$ @Turksarama True, but it's not particularly reasonable to assume dragons will fly like hummingbirds - they'll want to exploit gliding and especially thermals as much as possible, like most large flyers. $\endgroup$
    – Luaan
    May 2, 2022 at 5:48
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    $\begingroup$ @Turksarama This is all very back of envelope. A continuous 12KN is the minimum for hovering, but depending on your aerodynamics you can engage in level flight with far less than that. For instance a goose in level flight has a thrust to weight ratio of 0.05. $\endgroup$
    – sphennings
    May 2, 2022 at 14:44
  • $\begingroup$ That's a good point about them wanting to glide and use thermals. I figure they might do that for longer distance flights to save their energy. I just wanted them to be capable of self-powered flight, doesn't mean that they will always use it if they don't have to. $\endgroup$
    – Arvex
    May 4, 2022 at 2:45
  • $\begingroup$ Great answer. The only thing I would add is the good old equal and opposite reaction isssue. If a dragon tries to use his wings as a directed attack he is going to push himself back just as hard. This renders any attempt to weaponize his propulsion pretty limited short of just flying over things and hoping the downwash was dangerous enough on it's own. $\endgroup$
    – dsollen
    May 6, 2022 at 2:09
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65 mph winds. If you stand REALLY close.

The wingspan is about 50 feet. So each wing is about 25 feet long. For simplicity let's say each wing is a triangle 25 feet long and oh I don't know. . . . 15 feet high?

Then the wing has surface area $(25 \times 15)/2$ square feet. There are two wings so the total flight surface is $25 \times 15 = 375$ square feet.

If the dragon weighs 2700 pounds then 3750 is a reasonable force. That's 1050 lbs of upwards force once you overcome gravity. So the pressure on the wing surface is $3750/375 = 10$ pounds per square inch.

The dragon flapping its wings generates a shockwave that pushes stuff over with pressure equal to 10 pounds per square foot. Looking at engineering charts suggests that's equivalent to windspeeds of about 65 mph.

Well that's assuming you are right next to the wing as it flaps. The shockwave will disperse as it travels further from the wing. So you get at most 65mph winds. Likely much less.

How strong is 65mph wind? Well here is a loud man in a wind tunnel to demonstrate.

It seems 70 mph won't take you off your feet if you lean slightly forwards and 65 mph is weaker than that. Note the man in the video is bald. That makes him more aerodynamic and better at resisting winds

Maybe 65 mph would knock you down if it took you off guard. The dragon would have to sneak up behind you and then take off suddenly without you noticing.

enter image description here

WELL HERE WE ARE NOW STRONG TROPICAL STORM FORCE

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Wing- clap. (Slight frame-challenge.)

Daron has done a splendid job of showing the calculation for mean force and mean windspeed. - But the dragon's not producing force continually, there's an upstroke, then a downstroke.

If the up and down strokes last the same length of time, then 120~ Mph "gusts" would be generated. If a downbeat is sudden and done with full force, then that might be doubled easily knocking over any nearby soldiers and cavalry. Of course, they can just get up again.

If, however, the wings are brought together in the front, back-edges meeting first, then the front tip-ends cracking together like a whip - this would result in a narrow, directed air blast and a supersonic crack proportional in magnitude to the size of the dragon's wings that executed it. Enough to deafen and disorient humans for several minutes, possibly enough to weaken and shake apart doors and other obstacles. I'm not suggesting that any damage should be done to horses here, but you could if you wanted.

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If they can fly, their wings can obviously produce a force equal to their weight: 2700 pounds, which is 1224 kg and about 12240 N.

If it wasn't so, they would not be able to leave the ground.

And if when they grow their wings grow slightly less than their bodies, it makes sense that the adults are less able to fly than the youngsters.

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  • $\begingroup$ Or even if the wings don't increase in relative size fast enough -- a dragon 50% larger in linear dimension needs wings 83% larger in linear dimension for the same flight capability. $\endgroup$
    – Charles
    May 2, 2022 at 3:25

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