Jul 21, 2009, 11:50 PM
Post #1 of 10
Introducing Wingsuit Studio, a revolutionary -- see, I do nothing but revolutionary stuff -- wingsuit flight analysis and modeling program.
Wingsuit Studio is expandable with custom "modules" designed to do specific task. They are based on Wingsuit Studio's framework which is centered around numerical Wingsuit Equations solver, Flight Library which allows you manage pilots, flight modes, and mountains, and Unit Library that handles unit conversions. The software development kit will be coming in the near future allowing programmers write their own modules.
Currently, 3 modules are included with the installation:
Shows derivation of Wingsuit Equations and solves them numerically.
Wingsuit Equations are differential equations of motion governing wingsuit flight dynamics in two dimensions. Simple and beautiful, they allow for high precision simulation of wingsuit flight by knowing sustained velocity alone.
This module shows the derivation of Wingsuit Equations and explores various aspects of wingsuit flight: trajectory, velocity, acceleration, glide ratio, and other properties of the flight.
To solve WSE numerically, the 4th-order Runge-Kutta method with integration step of 0.1s is used. Solving WSE is handled by Wingsuit.Equations.dll .NET class library which you can freely use for your own Wingsuit Studio modules and other projects.
Calculates average L/D from BASE jump distance, height and time using Wingsuit Equations.
L/D Calculator is the most consistent and accurate way of estimating your L/D from a BASE jump. To use it, you need to measure distance, height, and time by using GPS or by wearing a video camera and passing close to a topographic feature which you can measure on topo maps. Note that the flight must be straight, no turns.
L/D Calculator samples various flight modes (flight mode is a combination of horizontal and vertical sustained speeds) and solves Wingsuit Equations for the duration of your flight (in assumption of constant flight mode) until it finds a mode that results in the closest match with the actual distance and altitude used on your jump.
L/D Calculator first uses "Hill Climbing" method of finding the solution, with a random seed between 0 and 150mph or 250km/h on the velocity grid. The step is gradually reduced until an accurate enough solution is found. This is a fast method, but sometimes it fails to find the best fit. If this happens, brutal force method is used which samples every node on the velocity grid and gradually reduces the step until satisfactory match is found.
Note that L/D Calculator normalizes sustained speeds to sea level and standard temperature.
Exit altitude and exit temperature have virtually no effect on the calculated L/D, but they do affect sustained speed. If your launch is very strong, estimate your launch speed and use it in calculation, as it affects calculated L/D.
The old technique of estimating L/D by subtracting some altitude used to start to fly from the available altitude and dividing the distance by this altitude gives inconsistent results, as the higher or the lower the mountain, the lower or the higher the contribution from the 'starting to fly' portion of the flight would be.
Using L/D Calculator for flights of various degree of performance and in different wingsuits allows you to build polar curves (collections of flight modes) which can be used in other modules.
World BASE Race
Helps you choose optimal flight mode for flying the World BASE Race (Romsdalen, Norway) in shortest time possible.
While there is no substitute for experience to win the World BASE Race in Romsdalen, Norway, the different modes of flying are too many to explore in limited time, and this is where World BASE Race module comes to help.
This is a tool that helps you answer questions like these:
- Do I need the highest L/D suit to win? - Is it better to do a steep dive to get more speed, or to start flying as soon as possible? - Is large, floaty suit or small, speedy suit better for the purpose? - Will losing or gaining weight (or using extra weights) help me shorten the time? - Do I stand any chance in a fast tracking suit?
The module uses Wingsuit Equations to simulate flights of two pilots based on their flight modes.
If this module does help you win the World BASE Race, send me a case of your favorite beer! ;-)
Also, Wingsuit Studio includes several sample pilots. Pilot is a collection of flight modes, and flight mode is a combination of sustained horizontal and vertical speeds normalized to sea level and normal temperature that characterizes wingsuit flight dynamics for specific pilot in specific suit at certain body position and angle of attack. These sample pilots will get you started, and you create your own pilots based on GPS data of your flights. Pilot files can easily be exchanged between users and imported into the Studio.
Wingsuit Studio (Windows only) can be downloaded here:
I haven't tried your software, but I've followed the links you posted to wingsuit equations.
The drag and lift coefficients (Cd and Cl) can indeed be treated as constant at a specific angle of attack, but this isn't a very useful property, since (as you noted) during a wingsuit flight, the AoA changes. You then use L/D vs. pitch tables to account for this effect.
There is a much better way to do this. Split the drag into induced drag and parasitic drag. Induced drag (D_i) is defined as that produced as a direct result of generating lift. It can be accurately modelled as:
D_i = L^2/(c_i*rho*V^2)
where L is lift, rho is air density, V is the speed of the wingsuit, and c_i is a constant (independent of AoA!)
Parasitic drag (D_p) can be defined as all the drag that is independent of lift (and also of AoA!)
D_p = c_p*rho*V^2
Again, c_p is a constant, independent of AoA.
If we let V_s be the sink speed (the component of the velocity pointing downward), then using Newton's equations, one can show that:
where g is acceleration due to gravity, and m is the mass of the wingsuit flyer. You can of course solve for V_s, but the equation is easier to verify in the form provided.
If you have V_s and V data from a GPS, then you can estimate c_i and c_p. You can then study all sorts of interesting properties of wingsuit flight without ever having to calculate the AoA! It would also be straightforward to modify the equation to model the non-equilibrium subterminal flight. Again, this could be done without worrying about AoA.
And if you really are interested in the AoA, you can work it out by using the fact that lift is a linear function of AoA (up to the stall point, of course).
Splitting the drag into two (or more) parts is more useful for aviators (i.e. powered, mostly sustained, flight) rather than gliders. It's like slicing the cake into several parts: you can call them different names, but together they're still the same cake.
If you read the "Derivation" tab in Wingsuit Equations module, you will see that the whole "pure fucking magic" is to abstract away from AoA and describe the dynamics of flight in terms of measurable quantities, such as sustained horizontal and vertical speeds. Modeling with variable flight modes is also possible (although not yet implemented in WSS). For example, to clear the ledge, you may start with the mode that pulls you away from the wall quickly, and that is the mode with rather poor L/D (about 1.0-1.5 - about 45 degree headdown pitch right after exit), and then kick in the max L/D mode. This can be modeled using WSE easily.
Wingsuit Studio has been updated with the new version of World BASE Race module.
The new version includes Optimizer which automatically finds the fastest flying mode for given L/D.
If you have already played with WBR module, you may have been wondering, "Well, what would be the fastest flying mode out there? what wingsuit, what kind of performance would result in absolutely fastest time?" Optimizer uses brutal force approach and tries all possible modes to find the best.
It turns out, the higher L/D, the better the time. So to be realistic, Optimizer uses L/D you set as a maximum L/D that it will not exceed while searching for faster finish times.
For given L/D, there exists an optimal flight mode (i.e. combination of sustained horizontal Vxs and vertical Vys speeds) that results in fastest time possible while satisfying the constraints (terrain + minimum pull altitude).
Here are the results (with minimum pull altitude of 300ft (~90m) and zero launch speed):
- tracking suits are out: no competition to wingsuits, several seconds behind
- WBR *is* mostly a L/D competition. Awesome! Anti-Marl'09, anti-mattress, anti-trackingderby all the way... as it should be to begin with. Schweet L/D, baby! A good test for different makes of wingsuits (besides, of course, being a test for different pilots). Wingsuit manufacturers, here's a good show to shine on!
- shortest finish times demand very fast (yet high L/D) flight modes. Heavier pilots with high wingloading (while maintaining L/D in 2.5-3.0 range) will have advantage over the light pilots.
- strong launch always helps (assuming pilot is capable of doing it without compromising efficient flying and safety). 5mph (~2m/s) launch speed results in about 0.3s shorter time.
- the fastest flight mode is that just skims the terrain about half-way to the finish line and just clears the minimum pull altitude. Note that this means "naturally" high L/D mode, not just diving down with average L/D intentionally and skimming the terrain and pulling low. Again, heavy jumpers with efficient L/D will have advantage, as after natural curve pullout they will be lower - but faster - than lighter jumpers.
- the spread between L/D of 2.5 and 3.0 is quite small, less than a second. Therefore, not only excellent flying skills, but ability to do a strong launch precisely at the starting gun matters a lot. Pilots with running/ski/swimming competition experience will have advantage over good pilots who never jumped by starting gun.
- moving WBR to a bigger mountain where the spread between the best pilots will be less "electronic" would be a better test of pilot's skills and wingsuit rating.
The flight modes calculated by Optimizer are at sea level, standard temperature (15 C). Use Flight Mode Converter from Tools menu to convert it to a different altitude. Typically, at 6000ft speeds are about 10-12% higher.
Download the updated Wingsuit Studio by clicking this icon:
The results predicted by Wingsuit Studio are spookily realistic. Compare to WBR2008 results:
Aug 23, 2009, 7:39 PM
Post #10 of 10
Example of using L/D Calculator and Wingsuit Equations modules
[In reply to]
Here's an example of using L/D Calculator:
Mt.Brento, pulling over the windsock by the bar (distance = 5300ft) at 550ft (altitude used = 3300ft) in 40s. Jumper: me in Phantom-1 and Razor with Trango 285, exit weight 250lbs, 6'1" tall.
Result: L/D = 2.27, Vxs = 98.8mph, Vys = 43.5mph (sustained speeds at sea level; at 6000ft, that is equivalent to approx. 109/48).
From jumps with less aerodynamic rigs, I found my L/D in Phantom to be about 2.1. A 10% improvement comes mostly from Razor/Trango.
If the sustained speeds are prorated proportionally to the square root of wingloading for a jumper with exit weight 180lbs (of same height), or Vxs = 83.8mph, Vys = 36.9mph (same L/D = 2.27), the opening altitude would be about 800ft and flight would be 45s long. (found by plugging the numbers into Wingsuit Equations module)
A flyer at L/D = 2.9, Vxs = 87mph, Vys = 30mph would end up pulling at 1300ft.
Feel a little measurbatory today? Post your flights!