Welcome, today’s class will be on one of the class off anime laws, specifically the one on aerodynamics.
Law of Topological Aerodynamics, First Law of Anime Aero-Dynamics– *ANY* shape, no matter how convoluted or odd-looking, is automatically aerodynamic. (Darrin Bright and Ryan Shellito)
Aerodynamics for anyone who doesn’t already know, is the study of the properties of moving air and objects that move through the air. So how is it that things fly through the air? When considering flight, you have to consider the four basic forces of flight.
Thrust- The force that moves the aircraft forward. It is generated by the engine and at the current time is generated by expelling the hot gasses created by jet engines out the back of the plane.
Gravity- The force pulling the object down
Lift- The force moving the object upward. Lift occurs whenever an object is moving through a fluid, and air is actually a fluid. Lift is why the curve ball works, and it is why an airplane can fly. Lift is improved when the object has wings and it is calculated using the following equation:
L = (1/2) dv2sCL
L = lift
D = density of the air
V = velocity of the aircraft
S = wing area of the aircraft
CL = coefficient of lift
The coefficient of lift is determined by the type of wing and the angle of attack. The angle of attack is the angle of the airfoil relative to the direction of the wind and can be seen in the diagram below.
Types of airfoils
Drag- The force that resists the object moving forward. For standard flight this force is air resistance or friction between the object and the air. It changes due to altitude, and wind.
Anime example 1
For our first example we will look at the core fighter from Mobile Suit Gundam 0079. The reason I am picking this for our first example is that due to its passing resemblance to a real aircraft, it should have some chance of flying.
Important technical details
Length– 8.6 m (28ft)
Width– 6.8 m (22ft)
Weight– 8.9 tons (19,600lbs)
Density of the air at sea level- 0.002377 lbm/ft3
Since as I could not find any numbers on the actual wing span of the core fighter, I will have to calculate one. I feel that the easiest and most accurate way to do this is to use the surface area of the bottom of the fighter and then cut that number by 50%. We can see from looking at the picture that plane will not cover the entirety of a square draw underneath it, so its wingspan will be less than the area of that square. I think that 50% is a good rough estimate for the purposes of this discussion.
Wing span- 308 ft2 (square feet is used because the equation I found said to use standard measurements and I am not an aeronautical engineer.)
Coefficient of lift- To my limited knowledge of aerodynamics it appears that this is unique to each type of aircraft. Since the core fighter is fictional aircraft with VTOL capabilities I used the F-35 as a reasonable real world equivalent. I also used a low angle of attack based on the relatively flat appearance of the wings of the core fighter in Gundam 0079. Thus the coefficient of lift is 0.2.
Velocity– Again using the F-35 as an equivalent, we will assume the maximum speed of the core fighter is mach 1.6 (1,228mph) or 1801 feet per second
Time for the math
L = (1/2) dv2sCL
L = (1/2) 0.002377 * 1,8012 * 308 * 0.2
L = 233,473 lbs
L = (1/2) dv2sCL
L = (1/2) 0.002377 * 5172 * 308 * 0.2
L = 19,600 lbs
The last step is to compare the lift generated by the aircraft to the weight of the aircraft. If the lift is equal to or greater than the weight of the plane, then it will be able to fly. Is this case I am rather surprised to say that the core fighter is actually able to fly based on its aerodynamics as long as it is able to move fast enough.
A stall in aerodynamics means that the wing is no longer generating lift and the plane is now falling out of the sky. This can occur due to a change in the attack angle of the wing, or a reduction in speed. The stall speed is the speed at which the plane is no longer traveling fast enough to generate lift. In the case of the core fighter the stall speed is 517mph which is quite high.
While the math proves that the core fighter can actually fly, I am going to call it plausible at this time, for three reasons.
1- The lack of information given on the core fighter
2- Very high stall speed for the core fighter
3- My lack of knowledge on aerodynamics
The main take aways here for many anime planes are going to be the size of the wing, and the speed of the aircraft. Many anime mecha designs lack significant wings which means unless they are traveling extremely fast it will simply be impossible for them to fly. To prove this let’s do the math for the Strike Freedom gundam and see just how big the wings have to be.
Lift needed- 176,000
Air density at sea level- 0.002337
Velocity- 1125 fps- I am going to assume that the gundam cannot go faster than the speed of sound, because the resulting shockwaves could potentially damage the gundam.
Wing area- unknown
Lift coefficient- 0.1- given the small oddly shaped wings I think it is safe to say that the number should be low
L = (1/2) dv2sCL
176,000 = 0.5 * 0.002337 * 11252 * s * 0.1
176,000 = 148 s
1,189 ft squared = s
Essentially the Strike Freedom gundam would need the wing area of a B-1B bomber in order to be able to fly with its rather poor aerodynamics. Since it is not this size, we can safely call the ability of the gundam to fly busted.
So far today’s lesson has focused on flight, and vehicles that actually fly. What about the mecha that can hover in the air. The same four forces that were previously discussed are still in play, but they have changed slightly.
As you can see in the above diagram lift and thrust have both been combined, as have weight and drag. Now the above diagram is for a helicopter, and it would work the same for a mecha trying to hover in the air. In the case of hovering we can discount lift and drag as they would have minimal effects in this case. Thus we will need the weight of the mecha and how much thrust it can generate to see if it can hover.
This time we will be using the infamous Wing gundam Zero from gundam wing. According to MAHQ the Wing Zero masses only 8,000kg, and is able to output 88,150kg of thrust so it is more than able to hover. However, there is a problem with the numbers. If we are looking at the ability to hover then we need to have it calculated in newtons or foot pounds to account for the force of gravity. In this case the Wing zero needs to generate 8,000 * 9.8 or 78,400 newtons of thrust. I am going to assume that the 88,150kg was mislabeled, as even at this amount of newtowns it would be enough to launch the gundam into space, which was something the other gundams were unable to do without help.
I did check several other gundams from different series and this information is often lacking. In the case of the Strike Freedom it would need to be able to output 784,000 netwons of thrust to match its 784,000 newtons of weight.
For comparison the second stage of the Atlas V rocket has 99,200 newtons of thrust, which only just a little more than the reported thrust of the Wing zero. The boosters on the Delta II rocket can output 628,300 newtons of thrust, which is less than the 784,000 newtons of thrust the Strike Freedom can put out. Note these numbers just indicate the ability to hover; the gundams would need to be able to put out even more thrust in order to make changes in altitude as shown in the anime.
I have to call the gundams and other mecha’s ability to hover busted, not because it is impossible for the thrust to be generated, the issue is the size of the motors and amount of fuel necessary to pull off the hover.
The complete lack of aerodynamics will preclude any mecha from being able to fly, and it will not be able to hover without large engines and equally large fuel tanks.