Separation Sim

This simulator uses discretized physics equations to demonstrate the difference between airspeed and groundspeed, and provide an exit spacing time calculator for a specified horizontal separation.


Perspective Control Button

The reference frame button allows you to switch between ground (camera on tripod) and airmass (camera under balloon) reference frame perspectives. See the physics discussion dialog for more info.


Pan Camera via Drag Gesture

Use the drag gesture anywhere in the sky to pan the camera.


Menu Button

The main menu button gives you access to Airspeed vs. Groundspeed visualization scenarios, Exit Spacing Calculator, and the Physics Discussion dialog


Visualize Airspeed vs. Groundspeed
Illustrative Scenarios
Custom Scenario
Airspeed
KTAS
Groundspeed
Knots

Exit Spacing Time

seconds
Horizontal Separation Target
ft
Aircraft Airspeed
KTAS
Group 1 Terminal Velocity
mph
Group 2 Terminal Velocity
mph

Separation Physics

Set minimum safe exit spacing time based on jump run airspeed, not groundspeed!

This sim positions the jumpers and calculates separation using real-time dicretized physics equations (double-integrated accelerations calculated via sums of forces on horizontal and vertical axes). Fortunately, you don't need to be a physics nerd to gain a conceptual understanding of why jump run airspeed, not groundspeed, matters for determining minimum safe exit spacing times! Conceptual understanding comes with examining what "wind" really is, reference frames, and the forces that create horizontal separation:


Wind

Think of wind as a large chunk of air ("airmass") moving relative to the ground. The cloud, house, and transparent grid patterns in the sky and grass are there to help you visualize movement of the airmass relative to the ground.


Reference Frames

Reference frames are a perspective from which you evaluate things, namely relative speed and position. The reference frame button allows you to switch between ground (camera on tripod) and airmass (camera attached to balloon) reference frame perspectives.

Your mind likely defaults to the ground reference frame because that's what you can see. That is, you probably naturally evaluate the speed/position of things using the ground as your zero speed/position reference. But there are other (equally) valid reference frames that are particularly useful in physics, one of which being the airmass reference frame. In the airmass frame, your perspective is synced with the airmass (0 airspeed), and the ground is moving relative to your frame of reference at the speed of the "wind". The view from a balloon, at rest relative to the airmass it's in, is a good way to visualize the airmass reference frame.


Forces

Why does the airmass reference frame matter? The only forces that create horizontal separation are aerodynamic (lift/drag). Lift and drag forces are exerted on you by the air when you're moving relative to the airmass (airspeed), and have nothing to do with groundspeed. Thus, if we want to visualize separation, we need to visualize speed and position relative to the airmass.

Once you're separated from the aircraft, drag pushes you horizontally away from other groups still in the aircraft (if the aircraft has airspeed), giving you a different horizontal position and velocity relative to the airmass than those still in the aircraft (independent of groundspeed). Once you're off the hill in a neutral freefall position, you're approximately "synced" with the airmass in the horizontal direction at a particular horizontal position in the airmass, and would appear to be moving at the "wind" horizontal speed when viewed from the ground reference frame. When other groups leave the aircraft at non-zero airspeed, they are at a different horizontal position in the airmass, even at zero jump run groundspeed. Note that due to varying drag profiles, different freefall disciplines can cover significantly different horizontal distances in the airmass before "syncing" with the airmass - exit order certainly matters!

Bringing it all together: play with groundspeed vs. airspeed scenarios and observe the affect they have on horizontal separation. Switch reference frames to check your understanding of relative speed and position. Focus on the horizontal speed of the aircraft/jumpers relative to the airmass grid.


Limitations

For the sake of visualization and simplicity, the sim treats the airmass between ground and jump run as homogenous from a wind perspective (1 wind layer). Wind in real life is rarely completely homogenous between the ground and jump run, and shearing wind layers near opening altitude can diminsh horizontal separation at opening time.

The sim also assumes that the freefall group maintains the same aerodynamic profile with respect to the free stream (relative wind) throughout the jump. This is a more accurate assumption for experienced groups whom upon exit, immediately begin flying on the relative wind in their intended orientation.

In the interest of visualization and conservation of computational resources, the sim only runs ~5k feet of freefall. Horizontal separation converges asymptotically on steady state value, and with any typical flight styles up to ~180mph terminal, horizontal separation errors aren't significant compared to sim running beyond ~5k feet of freefall.

The sim performs force calculations and velocity/position integrations on .04s simulated time intervals, giving small position and velocity drift errors over simulated time.

With these limitations in mind, estimating opening altitude horizontal separation via jump run airspeed (i.e. physics) still yields a far more reliable approximation than doing so with jump run groundspeed. The err in relying on groundspeed is highlighted when comparing differing groundspeed illustrative scenarios configured with the airspeed vs. groundspeed dialog in this sim.


Under the hood (for the nerds)
Governing Force Equations: Force_Drag = 0.5 * Fluid_Density * Speed_Relative_to_Fluid ^ 2 * Coefficient_of_Drag * Reference_Area
Force_Gravity = mass * acceleration_gravity
1. Find aerodynamic coefficients via terminal velocity force sum: Sum_Vertical_Forces_Terminal = 0 = Force_Drag + Force_Gravity
Rearranging Sum of Vertical Forces at Terminal: Coefficient_of_Drag * Reference_Area = -Force_Gravity / (0.5 * Fluid_Density * Terminal_airspeed ^ 2)
2. Calculate drag force at this time step of simulation: Force_Drag (in direction opposite to total airspeed vector) = 0.5 * (Coefficient_of_Drag * Reference_Area) * Air_Density * Total_airspeed ^ 2
3. Calculate Sum of forces at this time step of simulation: Airspeed_angle = arctangent(vertical_airspeed / horizontal_airspeed)
Sum_Vertical_Forces = Force_Drag * sin(Airspeed_angle) - mass * accel_gravity
Sum_Horizontal_Forces = Force_Drag * cos(Airspeed_angle)
4. Calculate acceleration, integrate velocity and position: Vertical_Accel = Sum_Vertical_Forces / mass Horizontal_Accel = Sum_Horizontal_Forces / mass
Vertical_Velocity += Vertical_Accel * iteration_timestep Horizontal_Velocity += Horizontal_Accel * iteration_timestep
Vertical_Position += Vertical_Velocity * iteration_timestep Horizontal_Position += Horizontal_Velocity * iteration_timestep

In a neutral body position at terminal velocity, we know that the force of drag = -force of gravity. Thus at terminal velocity, we can solve for aerodynamic coefficients (product of: Coefficient of Drag * Reference Area).

Once we have the product of drag coeff * ref area, we can calculate drag force at any velocity with assumption that the group maintains same body position with respect to the free stream ("relative wind").

Total drag force at every iteration is then broken into horizontal and vertical components (using angle between previous iteration's horizontal and vertical airspeed components).

Dividing the sum of forces in horizontal and vertical directions by mass gives new horizontal and vertical acceleration, respectively.

Horizontal and Vertical velocity is then incremented by new respective acceleration * iteration timestep.

Finally, Horizontal and Vertical position is then incremented by new respective velocity * iteration timestep.

Credits

Thank you to all of my skydiving friends who have taken the time to give me thoughtful feedback and feature ideas: Jen, Liberty, and many others!