Back from Australia and the OLC Equation

My trip to Australia was a big success. I flew with Jim Staniforth in Lake Keepit's beautiful Duo Discus. We flew for 24 total hours over 6 days. Flying a 500km task, a 400km task, 3 300km tasks and one local area flight. It was a great learning experience, flying in very differing weather conditions. Lesson learned - fly dual with another cross country pilot whenever you can. There is no better way I can think of bettering your flying.

On to an equally interesting topic. I was flying for the first time this year from a soaring site in the US where I had a chance to place in the top 50 in the OLC distance competition (rules). It raised an interesting question, what would my average point score have to be to place in the top 50? I found the results interesting and I thought I would share them here.

To my surprise, the average score for the first 200 pilots in the United States is defined, very accurately, by an exponential equation. The equation is:

Average flight points = -132.9*ln(Your standing)+1100.9
Note: ln is the natural log

The equation is found by importing data from the top 200 pilots in the US into excel and applying a simple curve fit to the data. The R^2 value, a measure of how well the equation fits the data (1 being a perfect fit), is .996! Looking at the data, the issue actually comes from the variance in the top 3 pilots, who usually fly predominately in wave or ridge lift. This represents a break from the generally homogeneous population of pilots posting mostly thermal flights with some wave and ridge. If you remove the top 3 pilots the equation holds true to a R^2 value of .999! So what does this mean? I take away that the general population of soaring pilots is fairly homogeneous and that there is a core group of top pilots who combine excellent flying skill with superb weather to achieve great flight scores.

This result actually encouraged me to run the same analysis on data from 2008 and 2007. The results were equally exciting. Each year can be explained by a simple exponential function which has good correlation to the the real data, however the change in the curve from year to year has a clear trend. See figure 1:

Figure 1

What figure 1 shows that the OLC in the US for cross country distance is getting more competitive. If you remove the top 3 pilots from each year ,I call this the Jim Payne factor, the results point ever more to a general trend of increased competition (i.e. moving from #15 in the us to #10 takes more points each year). Also, to be in the top 50 requires the pilot to average ~25 more points per flight. Congratulations US pilots, you are getting better at flying, or more realistically more pilots are posting to the OLC, either way both are good things!

For you international pilots out there if you would like to perform this analysis for your country feel free to contact me and i can send you the excel files to get the results. Also this will not be my last post regarding the OLC, I have does some research developing a tool to locate thermals from multiple flight and map "hot spots" as a function of time of year and time of day. Not a new idea, but plenty of good results non the less!

Keep soaring (and posting to the OLC)
Michael

Off to Australia...

All,

I'm sorry that I missed posting last Sunday's entry on the secret OLC equation, I still have that information but I will be holding off until I return from my soaring adventure to Australia. I'll be flying a Duo Discus with a friend of mine out of Lake Keepit Soaring Club. Hope for hot temps and strong thermals! Look for lots of photos and maybe a few videos of the adventure when I return.

Keep soaring (even if it's winter where you live),
Michael

Total Energy Compensation Explained: Part II

We left off last week with the conclusion that for accurate total energy compensation a known coefficient of pressure of -1 is required somewhere on the aircraft. This weeks post will cover how to utilize that conclusion to give accurate total energy variometer readings. Today's post relies heavily on information gathered from NASA Technical Memorandum 73928, which can be found here.

A topic often covered in introduction to aerodynamics courses is the study of the flow field around a cylinder Link 1, Link 2. The body of knowledge regarding the velocity and pressure fields that surround a cylinder in cross flow is quite extensive. This body of work can be exploited for our study of the total energy probe given that the coefficient of pressure on the aft side of a cylinder is -1 under specific conditions. Below is a graph taken from this resource. This information is telling us that only for sub critical Reynolds numbers [less than 1.86x10^5] is the coefficient of pressure -1 on the aft side of the cylinder. It was this basic conclusion that led to the development of the small diameter total energy probe that we are familiar with today, however the detailed design of the probe was only developed after significant wind tunnel and empirical research. The following conclusions, taken directly from NASA TH X-73928, describes the other subtleties associated with an accurate total energy probe. These should give the average reader the tools to check and make sure their total energy probes are set up correctly.

1. Cylindrical tube, diameter o f 3/16- to 1/4-inch.
2. Tube end squared off with very slight bevel of sharp edge.
3. A f t facing pressure orifice , adrilled hole about 1/3 the tube diameter (1/16- to 3/32-inch).
4. Center of hole located a t a distance two times the tube diameter from the end of the tube (3/8- t o 1/2-inch).
5. Probe swept forward about 20 degrees with respect to flow direction.
6. Probe mounted in free-stream air, extending a minimum of 5 to 6 inches from the aircraft.
7. Vertical tail location good; aft fuselage acceptable.

Additional important is the rage of accurate operation:

1. 40-150 mph
2. sea level to 20,000'
3. Normal yaw and pitch attitudes (+/- 10 deg yaw, -5 to -25 deg pitch, hence the forward bend in the TE Probe to get a net +/- 5 degree invariance to pitch)

Most importantly, the total drag of the TE probe was found to be around 1/10 of a pound at 100 mph.

As important as the TE probe, the capacity bottle that is on the other side of the variometer needs to meet the design assumption made in last weeks post. If you remember we needed to assume constant density to develop the equations that allow up to exploit the properties if a Cp = -1. For that assumption to hold true we need to ensure the volume of air contained in the capacity bottle changes temperature (density) as slowly as possible. This is achieved by putting chore girl steel wool pads in the capacity bottles. The steel provides a good heat capacity to supply and absorb temperature differences.

Hopefully these posts will help you better understand the mechanics underway in the instruments used in soaring flight and help trouble shoot any potential issues in the future. Next weeks post will cover the mechanics of the online contest World Champion contest and how it proves that the number of quality of X/C soaring pilots in the United States is increasing. Until then...

Keep soaring,
Michael

Total Energy Compensation Explained: Part I

Most every pilot will tell you that a good total energy (TE) compensated variometer is essential for soaring flight. But how and why does it work? Total energy compensation, in the form commonly used in sailplanes today (capacity bottle and bent probe), was developed and patented by Oran Nicks (Patent Link) in 1977. Prior to that, G.E. Moore had done extensive research (Link 1, Link 2) investigating a way to combine both pitot and static pressure signals to compensate changes in static pressure (height gain/loss) with changes in airspeed (pitot pressure) to give the pilot an indication of the energy state, or total energy gain/loss, of the sailplane. The problem was that the device was complicated, expensive, and needed to be tested and adjusted to achieve accurate readings. It was Oran Nicks that saved us from this situation by discovering that the total energy of a sailplane is related to a unique pressure that can easily be measured independent of the pitot and static pressure input. The following proof will derive that pressure. For further reading see page 149 in Helmut Reichmann's Cross-Country Soaring.

Problem: We want to find a pressure (P*) that directly correlates with the total Energy (TE) of the sailplane.

Given: Dynamic pressure (P_dynamic), Static Pressure (P_stat)

Find: The change in Total Energy of the sailplane (delta_TE) as a function of an measurable change in pressure delta_P*.

Assume: We are flying in still air in a glider with an infinite glide ratio (no energy is lost to drag). In a glider with an infinite glide ratio, all kinetic energy (KE) can be transferred to potential energy (PE) and back to KE with out any losses (KE<==>PE, delta_TE=0).

Proof:

1) TE=KE+PE (total energy is the sum of the kinetic and potential energy)
2) delta_TE=delta_KE+delta_PE (the change in total energy is the sum of the change in both kinetic and potential energy)
3) 0 = delta_KE + delta_PE (since we assumed delta_TE = 0)
4) 0 = 1/2*m*delta_v^2 + m*g*delta_h (delta_KE = change in dynamic pressure [airspeed], delta_PE = change in static pressure [altitude], m = mass of air, g = gravitational constant)
5) 0 = 1/2*rho*delta_v^2 + rho*g*delta_h (4 divided by volume of air, rho = air density [assumed constant])
6) 0 = delta_P_dynamic - delta_P_stat (We know dynamic pressure is 1/2*rho*v^2, we also know static pressure is -rho*g*h, negative because pressure decreases with increasing h)
7) 0 = -delta_P_dynamic + delta_P_stat (multiply both sides by -1)

Read this to understand the source of equation 8.

8) Cp* = (P* - P_stat)/(P_dynamic) (the coefficient of pressure Cp* is the difference between the target pressure (P*) and static pressure divided by dynamic pressure.
9) Cp* = (delta_P* - delta_P_stat)/(delta_P_dynamic) (take the change in pressures)
10) delta_P* = (Cp*) * delta_P_dynamic + delta_P_stat (solve 9 for delta_P*)
11) if Cp* = -1, delta_p* = -delta_P_dynamic + delta_P_stat

This is where we see that if Cp* = -1, equation 11 and equation 7 are the same. This is what we want because delta_P* should represent the change in total energy, which we have already said is zero.

You can re-derive these equation without the assumption that delta_TE = 0 and you will find that delta_TE = -delta_P* (the negative originates for step 7). This was the amazing discovery that allowed for simple total energy compensation. delta_P*, the change in pressure associated with a coefficient of pressure of -1 represents the change in total energy of the sailplane. The result that a Cp* of -1 is required for total energy compensation is the reason for the shape of the total energy probe. One final point is required, rho (air density) was assumed constant in step 5, which is not exactly the case, however additional steps can be made in the design of a TE system to help achieve a relatively constant air density. Those techniques will be address along with how a Cp of -1 relates to the design of the TE probe in a future blog post.

This proof is a bit lengthy, however it is was an important discovery to soaring, please post any questions or comments and I'll do my best to answer them.

Keep soaring,
Michael

The First Thermal is Always the Hardest

With 170 hours in the cockpit this summer, I have greatly expanded both my depth and breadth of soaring experiences. But as I stand around the glider port here in Tehachapi, Ca I often cross paths with pilots who have been flying longer than I have even been alive; I clearly have a long way to go! So the question becomes; how do you catch up without losing your job for taking too many “blue flu” days? I believe the answer lays in a rule of thumb from back in college, “for every hour spent in class you should spend 2 hours studying”. So I figure I need to spend 340 hours this winter studying soaring. Lucky for me, along with a love of airplanes and flying I was born an engineer, and engineers love to analyze data. Now that the sun is setting earlier and earlier, the thermals are drying up, and the winds are starting to blow I have more time to research and read about the science of soaring flight. That’s where the idea for this blog originated; The Soaring Laboratory will capture all the interesting ideas, data, and results that I develop or find as I press forward with my study of soaring. Some articles will be original works, some will rely heavily on the work done by others, and some will bring together the voices various pilots on soaring technique. The articles will follow the rigor required of scientific study, however great effort will be made for the major points and any conclusions to be clearly stated for all to understand. I may even add humor if I think people are actually reading what I am writing.

For an example of the type of information to be presented I would like to share a website that I found very interesting. It answers the question, “what would it look like if a large selection of soaring flights from 1997 to 2003 from around the world were plotted on one map?” The website (http://www.pfg.dk/termikanalyse/) is the product of a Denmark soaring club called Polytechnic Flight Group, I would suggest using this link for the translated version of their website. The source of the plotted flight data is unclear for years 1997-2002. The 2003 data appears to be from the OLC and amazing learning resource and a topic of a future blog post. For now enjoy sifting through the data; I find it very interesting the amazing disparity in the number of flight in Germany as compared to the rest of the world. For the time period studied, Germany accounted for 20912 flights, about 2 times the 2^nd place country, Austria. However because the data source and collection methods are ambiguous only general trends can evaluated. Here is an image of all flights in North America.

Keep soaring,
Michael