arkie87

So, Bill Nye recently put up another video about deflate-gate where he attempts to tackle the issue of whether or not the plummeting temperature could have reduced the ball pressure. Here is the video: http://www.funnyordie.com/videos/3d0c94936c/bill-nye-addresses-deflategate Some background information: Internal pressure of the ball must be between 12.5-13.5 psi Balls were found to be 2 psi below requirements. Inside temperature might have been up to 80F (300K) , and outside temperature was around 50F (283K) that night. He claims a 6% pressure drop by calculating the ratio of temperatures i.e. 1- 50F/80F = 1 - 283 K/ 300K ~ 5.5%. This is correct. He then claims that this is off by a factor of 2.5. I assume what he means is 6%*13 psi = 0.78 psi, and 0.78 psi * 2.5 = 1.95 psi, which is close to the 2 psi deflation the league officials found. However, he should not be using 13 psi, since this is gauge pressure; he needs to use absolute, which requires adding 14.7 psi. Thus, 6%*(13+14.7) = 1.662 psi, which is close to the 2 psi deflation the league found (and not a factor of 2.5). Thoughts? Did i do a miscalculation somewhere? PS: please only comment about the calculations, not about the controversy, or whether or not you think the patriots did it etc...

I know! But this must have been the moment he heard of it

And a tweakable option for percent covered in solar panels and heat shield

Science is the easiest to rationalize! Having scientists on board results in more science, since they can analyze the data/collect the data better before transmitting.... isnt that obvious? And the game should automatically tell you there is an experiment you have on board that you can do for science... so i think a better lvl 5 ability is desired

There probably arent analytical methods for more complex shapes (at least not without simplifying assumptions). The purpose of that exercise was to figure out, in general, how we define drag and lift coefficient, which area we use, and whether area or coefficient changes with AoA.

Yeah, this whole exercise has made me seriously think about lift and drag, but i think using the exact solution for a flat plate has helped me to understand the corrected definitions. Since a flat plate has no projection (at zero angle of attack), there is only drag and lift for non-zero angle of attack (AoA). As far as i can tell, the analytical (?) solutions for C_D and C_l are known to be: C_D = 1- cos(2*AoA) C_L = sin(2*AoA) which looks like this. I can derive these equations if i make the following assumptions: (1) The magnitude of the force on the flat plate is proportional to 2 times the dynamic pressure and the projected area i.e. A*sin(AoA) and not reference area (A) (2) The direction of the force is always parallel to area normal vector #2 is pretty self intuitive since the force, resulting from stagnation pressure, is applied perpendicular to the surface which it acts upon i.e. parallel to the surface normal vector. #1, on the other hand, is a bit trickier. At first glance, you might assume that the magnitude of the force must be proportional to the reference area, and not the projected area, since the pressure acts upon the whole reference area and not just the projected area. However, for the case of zero AoA, there is zero force, and this wouldnt be the case if we used reference area (since force would be constant with AoA). Thus, using projected area seems better suited. Furthermore, the reason for taking two times the dynamic pressure is since it is assumed that on the side of the plate facing the flow, the pressure is equal to positive the dynamic pressure, whereas on the side of the plate away from the flow, the pressure is negative the dynamic pressure. Thus, the pressure difference is 2 times the dynamic pressure. Thus, from #1: F = 1/2 rho V^2 * 2 A sin(AoA) And #2: Drag = F*sin(AoA) Lift = F*cos(AoA) We find that: Drag = 1/2 rho V^2 * 2 A (sin(AoA))^2 = 1/2 rho V^2 A C_D And: Lift = 1/2 rho V^2 * 2 A cos(AoA)*sin(AoA) = 1/2 rho V^2 A C_L Comparing this result to the definitions of drag and lift coefficients: Drag = 1/2 rho V^2 A C_D Lift = 1/2 rho V^2 A C_L We find: C_D = 2 (sin(AoA))^2 ==> 1 - cos(2*AoA) via trig. identity And: C_L = 2 cos(AoA)*sin(AoA) ==> sin(2*AoA) via trig. identity Thus, it is apparent that reference area is held constant in lift and drag formulas and it is the C_D and C_L that change with AoA (rather than area). However, this definition makes sense for wings only, since area facing flow at zero AoA is very small compared to area perpendicular to the flow. Furthermore, the reference you supplied mentioned that it is convenient to use the same reference area for wings since then the ratio of lift-to-drag force (which is often of interest to aerospace engineers) is proportional to the ratio of the lift-to-drag coefficients. For non-wings, the definitions of C_D and C_L might use difference reference areas. However, i would be surprised if any body required calculation of projected area-- even for drag; instead, i would think C_D would be adjusted accordingly for convenience (i.e. whats the point of defining C_D such that when AoA changes, you must calculate a new C_D and a new area when you can define C_D such that it takes new area into consideration so that when AoA changes, you only need a new C_D?)

Both C_D and C_L are complicated and require CFD to get accurate results for all AoA and Mach numbers, but this is irrelevant to our definition of them. We can choose to define them however we want, based on whatever way is most convenient. It would make sense, that their definitions should be analogous to each other i.e. area is constant, but you are suggesting area is parallel (i.e. frontal) for drag and varies with AoA, while it is constant and perpendicular (i.e. wing) area for lift. Meanwhile, the reference ive shown implies for a horizontal flat plate, lift and drag coefficient always use wing area and wing area is held constant with AoA... so something is inconsistent... F=m*a... It will still have translational acceleration even drag/lift force(s) act off center of mass. I think you are confused because you imagine it spinning around wildly (in which case, it will have no net translational acceleration). However, this isnt necessarily the case: how wildly/fast it rotates depends on how offset force is from center of mass as well as how large/small moment of inertia is. If moment of inertia is large, rocket will translate more than it rotates. Just because there is no counter torque to arrest rotation, doesnt mean the craft cannot have translational acceleration. You can push tall objects significantly off-CoM, and still accelerate them horizontally (though they will always rotate as well). Besides, in reality, spacecraft have control surfaces, reaction wheels, RCS, and thrust vectoring to provide counter-torques to arrest rotation. If these counter torques are applied with forces far offset from CoM, then they will negligibly cancel out horizontal acceleration.

Do you have a reference for this? Why should C_D be constant but not C_L w.r.t. AoA? According to this reference, C_D and C_L are a function of AoA for a flat plate (though i dont see any good reason why this wouldnt be the case for other shapes as well). There would be translation and rotation (btw, this would happen for lift as well...). Once again, if that is what the physics predicts will happen, then imposing "corrections" will cause the model to depart from reality, which is usually bad (unless that is what you are going after).

I wonder if they use stock aero, NEAR, or FAR...

I was building my model mostly for fun, to help you, and to potentially optimize ascent trajectory with FAR installed. It's not "difficult" its just that I couldnt find a reference to the general form of the momentum conservation equations with with non-zero AoA and non-horizontal velocity vector. My frustration with just deriving the equations myself stems from my uncertainty regarding the definition/use of C_D and C_L I.e. is lift always vertical and drag always horizontal regardless of velocity vector? I also wasnt sure if reference area changed with AoA, or if C_D and C_L values changed accordingly such to keep reference area constant. After looking into C_D and C_L for a flat plate, it seems that reference area is always constant i.e. C_D and C_L are adjusted rather than adjusting reference area, and i am fairly certain that lift and drag always point perpendicular and parallel to velocity vector, respectively.

To compare euler, euler-cromer, and RK, i used simple mass-on-spring system, since the point was to show that euler eventually diverges regardless of time step, while euler-cromer and RK are unconditionally stable (regardless of timestep). I have created a few flight models (in excel and Matlab), but am having trouble deciding what the correct form of the equations should be... perhaps i should just bother ferram...

(1) You misunderstand: if you click on the reference, there is a slightly modified algorithm (Euler-Cromer's Method) which is formulated to conserve energy. You do not have to add this in as a constraint. (all you have to do is use euler, but use x = x + v(k+1)*dt instead of v(k)*dt ) EDIT: it conserves energy to tolerance based on step used. I have tested regular Euler, Euler-Cromer and 4th order runge-kutta, and while regular Euler is unstable and diverges after only a few iterations, Euler-Cromer (and obviously Runge-Kutta) are stable even after thousands of periods. (2) I think if with 4th order or Euler-Cromer method you conserve energy, then you are solving the physics itself. If the system oscillates, it oscillates... (though in real life, this oscillation is damped by pilot/autopilot using control surfaces).

So you said before that 1st order euler is unstable for harmonic motion. It seems like you are right, and it is known to not conserve energy. However, according to this reference, you can used a modified version of euler, which will conserve energy.

Angle of attack formula is incorrect as written (might just be a typo); should be x'j/x'i not xj/xi (Same problem with projected area formula) also, an easy way to get around the changing sign of drag if velocity is negative part is to use: abs(v)*v instead of v^2 i.e. F_drag = -C*abs(v)*v (since drag starts out negative) For components, this isnt necessary since v=sqrt(vx^2+vy^2) >=0

3rd order runge-kutta? I've heard of 4th, but not third. I'm not convinced its due to integration order or lack of "component" drag. I've modeled component drag, and i still get oscillations. How do you model drag and/or lift? Do you account for area difference when off 0 degree AoA? Do you account for fulcrum distance changing with changing angle?

To clarify, you said: Emphasis mine. So by doing the math you mean calculating the actual moment of inertia, as opposed to just adding in a constant, but non-zero moment of inertia term, which is what you did, and will prevent oscillations from going to infinity. And which behavior are you not seeing/who are you responding to?

What is FRC? Why are you relegated to using stokes drag (rules of the competition or giving up)? Either way, I'd say doing all that in high school is quite impressive... - - - Updated - - - When you say you didnt add math for moment of inertia, you mean you assume moment of inertia is zero, or moment of inertia is some small, but finite number, because if its zero, the rocket will never be stable numerically, since any torque will produce infinite angular acceleration...

I dont think adding in moment of inertia terms will help, since although it will take longer for the oscillations to form, they will also be harder to stop, since they will have much more inertia.. Why is F_x = C*v_total*V_y and not: F_x = C*v_total^2 * cos(theta) and F_y = C*V_total^2 * sin(theta)?

I think for the satellite placing and/or base contracts, i think once you complete the contract, you lost "control" of the satellite/station, such that you cannot fly it anymore. This will be easy to implement once they add multiplayer, since the satellite and/or station will behave just like another player "owns" it, such that you cannot take control of it. I think this will both add realism (once you deliver on the contract, you hand the base/satellite over to the company that paid you) as well as prevent clutter, from having six minmus bases and 5 mun bases etc...

Yeah, i think that is what happened, and ive noticed "phantom torques" a lot, but i think it was just trim. I think i need to attach trim to a new button, since sometimes i force physical time warp (alt+< or alt+>) while flying the craft i.e. pressing asfwqe keys

This might be related/unrelated, but I've noticed that vehicles are also *too* unstable on their own, without SAS, as if they generate their own forces... For example, i had a craft landed on minmus. As soon as i disembarked the pilot, since there was no SAS, the craft was left on its own, and it flipped over, despite being on flat terrain with a wide base...

There is an analytical solution, since the non-dimensional case got a solution, and Wolfram Alpha can provide it Let me know what result you get... - - - Updated - - - An Excel Spreadsheet with a Macro to solve for the burn time can be found here: here

I think the problem is the use of arctan instead of arcsin. See this Though it looks like you found that already... I dont think its possible to solve for t without using Excel's solver or a macro. I can make a macro button which will solve for the t needed. How does that sound? - - - Updated - - - In good faith, here are my results:

Use Wolfram Alpha to integrate it. It gave me an analytical solution (though matlab gave up)