In this paper we calculate the minimum area and length of a dragon’s wing for it to be able to fly. The minimum area was calculated to be 224m^2 and the length was 35.6m

Cobley, D

Fenlon-Smith, D

Jupp, M

Yeomans, K

English

University of Leicester Open Journals

Journal of Physics Special TopicsAn undergraduate physics journalP4 2 How to fly your dragonD.Fenlon-Smith, M.Jupp, K.Yeomans, D.CobleyDepartment of Physics and Astronomy, University of Leicester, Leicester, LE1 7RHOctober 27, 2016AbstractIn this paper we calculate the minimum area and length of a dragons wing for it to be able to fly. Theminimum area was calculated to be 224m2 and the wingspan 71.2m.IntroductionDragons are found in many myths and legendsand are also commonly found in video games andtable top fantasy games. Dragons are knownfor their large size, this leads to the interestingquestion of how large a dragon’s wings wouldneed to be to support its weight while in flight.For this we look at the common ’western’ styleof dragon with four legs and two wings, as theeastern style of more serpentine, wingless drag-ons flight is more closely related to magic. Thedragon used in these calculations will be basedon dragons found in the Dungeons & Dragons5th Edition (D&D) game.To calculate the required wing size, we must as-sume a manner of flight, for this article we willcompare dragons to large birds, due to both be-ing large winged creatures of reptilian origin, thismeans it would spend most of its time in the airgliding, as it takes large amounts of energy to usits wings to keep itself air-borne. This enables usto model the wings as aerofoils, to a reasonableapproximation, this means that the lift force pro-vided by the wings can be calculated by equation(1)[1];Fl = ClAρv22(1)where n is the increased length along the topside of the wing, A is the area of the wings, ρ isthe density of the air and v is the velocity of thedragon. This lift force needs to be greater thanor equal to the downward force from gravity onthe dragon. As these dragons are assumed to usethe same mechanics as large birds for flight thispaper will not calculate if a dragon could takeoff from the ground, as we assume that like largebirds they would also need to use thermals [2].For flight to be possible the force of lift on adragon while flying would have to be greaterthan or equal to the downward force due to grav-ity which is calculated using F = mg where m isthe mass of the dragon and g = 9.81ms−2. It wasassumed that HP, a value roughly approximat-ing the life of a creature that is often related tosize for larger creatures, was linearly related tothe mass of larger creatures. Using this assump-tion the average of all adult dragons HP in thegame was compared to the HP of an Allosaurus.This was done because an Allosaurus would havehad a body structure comparable to that of west-ern dragons and estimates of the mass of an Al-losaurus have been calculated [3]. An Allosauruswas thought to have had a mass of 2.3 tons [3]and it has a HP of 51 [4], the average dragonHP of adult dragons is 215, this would give theaverage mass of adult dragons to be approxi-mately 9696kg. From equation (??) this givesthe weight of the dragon as F = 95118N. In com-bat a dragon can fly, at maximum, 160 feet in a‘turn. A ‘turn is a 6 second period of time thusthe maximum combat flight speed is 26.6 feet persecond. The speeds in D&D are written such acreature that can move 120 feet in a turn, incombat, can move at 100 feet per second out ofcombat. This means that the max flying speedof a dragon is 133 feet per second or 40.6ms−2.The surface area of the dragon’s wings wasthen calculated to be 448m2 using equation (1),setting Fl to be equal to the weight of the dragon,v = 40.6ms−2, ρ = 1.225kgm−3 and assuming aCl of 0.21. This surface area is the combined to-tal for both the dragon’s wings, giving each winga surface area of A = 224m2. Therefore the areafor each wing is A = 224m2. To calculate thelength of the wing we need to assume a width,for this the length of different body parts needto be found. From the D&D monster manual [4]the length of the neck and head can be taken tobe about 2m long, the body about 5m and thetail about 4m long, giving the total length of thedragon to be roughly 11m. The wings have beenassumed to be roughly oval in shape as shownby figure 1 which means if the wing is assumedto be 8m across, equation (2)A = abpi (2)gives a ’b’ of 17.8m, giving a total wing lengthof 35.6m and a total wingspan of just over 71m.ConclusionWe have found that the length of a dragons wingwould need to be a minimum of 35.6m for itto be able to maintain flight, while this lengthis about three times longer than the distanceFigure 1: An Illustration of a dragon highlighting theoval-like shape of its wings.from its nose to tail it may still be plausible, assome large birds have a ration of about half this[5], but whose bodies are much less dense. It isworth noting that depending on the method offire breathing that is applied to the dragon, oilor gas, the dragon may have large volumes of hy-drogen stored in its body which would allow forslightly reduced wing size, An effect that maymerit further study.References[1] https://www.grc.nasa.gov/www/k-12/airplane/lifteq.html[2] https://www.quora.com/How-do-the-largest-flying-birds-get-airborne-Do-they-need-a-running-start-Is-it-any-different-from-how-sparrow-sized-birds-are-able-to-just-take-off-seemingly-instantly,11/10/2016[3] https://en.wikipedia.org/wiki/Allosaurus[4] Wizards of the coast Monster Manual (2014)[5] http://hubpages.com/animals/top-10-largest-birds-on-earth-wingspans

P4_2 How to fly your dragon

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P4_2 How to fly your dragon

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