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
November 18, 2009
November 8, 2009
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. - Cylindrical tube, diameter o f 3/16- to 1/4-inch.
- Tube end squared off with very slight bevel of sharp edge.
- A f t facing pressure orifice , adrilled hole about 1/3 the tube diameter (1/16- to 3/32-inch).
- 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).
- Probe swept forward about 20 degrees with respect to flow direction.
- Probe mounted in free-stream air, extending a minimum of 5 to 6 inches from the aircraft.
- Vertical tail location good; aft fuselage acceptable.
- 40-150 mph
- sea level to 20,000'
- 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)
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
November 1, 2009
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
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
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