(L/D)max vs. minimum total drag
01-06-2021, 01:47 PM
#11
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Joined APC: Jul 2008
Position: 747 Captain (Ret,)
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Harry Hurt did not make many mistakes when writing Aerodynamics for Naval Aviators, but he sure blew this one.
His chart clearly confuses min drag for L/D max.
I have also seen other publications which make the same mistake, possibly after reading Harry's book.
Note: While the min drag speed is theoretically the optimum holding speed, no human pilot, and very few autothrottle systems can actually control speed that well. For this reason, many aircraft flight manuals chart a slightly higher speed for optimum holding speed. For some aircraft, this slightly higher speed might actually be L/D max.
Joe
His chart clearly confuses min drag for L/D max.
I have also seen other publications which make the same mistake, possibly after reading Harry's book.
Note: While the min drag speed is theoretically the optimum holding speed, no human pilot, and very few autothrottle systems can actually control speed that well. For this reason, many aircraft flight manuals chart a slightly higher speed for optimum holding speed. For some aircraft, this slightly higher speed might actually be L/D max.
Joe
01-06-2021, 01:57 PM
#12
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Posts: 5,171
Actually, he didn’t. Look at page 98, there’s a fundamental difference between propeller and jet aircraft on their drag polars and where min drag occurs and where L/D Max occurs due to the form of propulsion—propellers do WORK, jet apply FORCE. Read thru it for the details.
01-06-2021, 09:16 PM
#13
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Joined APC: Jul 2005
Posts: 248
Galaxy is correct. When considering a Thrust Required curve, the lowest point is L/D max, whether piston or jet airplane. However, when determining Max Range and Max endurance, a piston airplane uses the Power Required curve, not Thrust required.
For a reciprocating engine, specific fuel consumption (commonly abbreviated SFC) is defined as the weight of fuel consumed per unit power per unit time. Anderson, John. Introduction to Flight (p. 501). McGraw-Hill Higher Education. Kindle Edition.
Thus Breguet Endurance and Range equations are determined from using Power Available versus Power Required curve. See attached. For a propeller airplane, maximum range is CL / CD max. Max endurance occurs at a CL^3/2 / CD max.
To maximize range for a reciprocating-engine, propeller-driven airplane, we want the following:
1. The largest possible propeller efficiency η.
2. The lowest possible specific fuel consumption c .
3. The highest ratio of W0 / W1 , which is obtained with the largest fuel weight WF .
4. Most importantly, flight at maximum L / D .
Anderson, John. Introduction to Flight (p. 505). McGraw-Hill Higher Education. Kindle Edition.
For a jet airplane, the Breguet Equations are derived from Thrust Required. As such, for jet airplanes CL / CD max corresponds to Max Endurance. Max range occurs at CL^1/2 / CD max.
to obtain maximum range for a jet airplane, we want the following:
1. Minimum thrust-specific fuel consumption ct .
2. Maximum fuel weight Wf .
3. Flight at maximum CL^1/2 / CD
4. Flight at high altitudes
Anderson, John. Introduction to Flight (p. 512). McGraw-Hill Higher Education. Kindle Edition.
For a reciprocating engine, specific fuel consumption (commonly abbreviated SFC) is defined as the weight of fuel consumed per unit power per unit time. Anderson, John. Introduction to Flight (p. 501). McGraw-Hill Higher Education. Kindle Edition.
Thus Breguet Endurance and Range equations are determined from using Power Available versus Power Required curve. See attached. For a propeller airplane, maximum range is CL / CD max. Max endurance occurs at a CL^3/2 / CD max.
To maximize range for a reciprocating-engine, propeller-driven airplane, we want the following:
1. The largest possible propeller efficiency η.
2. The lowest possible specific fuel consumption c .
3. The highest ratio of W0 / W1 , which is obtained with the largest fuel weight WF .
4. Most importantly, flight at maximum L / D .
Anderson, John. Introduction to Flight (p. 505). McGraw-Hill Higher Education. Kindle Edition.
For a jet airplane, the Breguet Equations are derived from Thrust Required. As such, for jet airplanes CL / CD max corresponds to Max Endurance. Max range occurs at CL^1/2 / CD max.
to obtain maximum range for a jet airplane, we want the following:
1. Minimum thrust-specific fuel consumption ct .
2. Maximum fuel weight Wf .
3. Flight at maximum CL^1/2 / CD
4. Flight at high altitudes
Anderson, John. Introduction to Flight (p. 512). McGraw-Hill Higher Education. Kindle Edition.
01-07-2021, 12:26 PM
#14
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Joined APC: Nov 2011
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Originally Posted by galaxy flyer
Somehow in the recesses of my brain, the correct answer is different for propeller versus jets. I need to look at “Aerodynamics for Naval Aviators”.
01-07-2021, 02:02 PM
#15
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Joined APC: Jan 2018
Posts: 1,676
Originally Posted by cougar
Galaxy is correct. When considering a Thrust Required curve, the lowest point is L/D max, whether piston or jet airplane. However, when determining Max Range and Max endurance, a piston airplane uses the Power Required curve, not Thrust required.
For a reciprocating engine, specific fuel consumption (commonly abbreviated SFC) is defined as the weight of fuel consumed per unit power per unit time. Anderson, John. Introduction to Flight (p. 501). McGraw-Hill Higher Education. Kindle Edition.
Thus Breguet Endurance and Range equations are determined from using Power Available versus Power Required curve. See attached. For a propeller airplane, maximum range is CL / CD max. Max endurance occurs at a CL^3/2 / CD max.
To maximize range for a reciprocating-engine, propeller-driven airplane, we want the following:
1. The largest possible propeller efficiency η.
2. The lowest possible specific fuel consumption c .
3. The highest ratio of W0 / W1 , which is obtained with the largest fuel weight WF .
4. Most importantly, flight at maximum L / D .
Anderson, John. Introduction to Flight (p. 505). McGraw-Hill Higher Education. Kindle Edition.
For a jet airplane, the Breguet Equations are derived from Thrust Required. As such, for jet airplanes CL / CD max corresponds to Max Endurance. Max range occurs at CL^1/2 / CD max.
to obtain maximum range for a jet airplane, we want the following:
1. Minimum thrust-specific fuel consumption ct .
2. Maximum fuel weight Wf .
3. Flight at maximum CL^1/2 / CD
4. Flight at high altitudes
Anderson, John. Introduction to Flight (p. 512). McGraw-Hill Higher Education. Kindle Edition.
For a reciprocating engine, specific fuel consumption (commonly abbreviated SFC) is defined as the weight of fuel consumed per unit power per unit time. Anderson, John. Introduction to Flight (p. 501). McGraw-Hill Higher Education. Kindle Edition.
Thus Breguet Endurance and Range equations are determined from using Power Available versus Power Required curve. See attached. For a propeller airplane, maximum range is CL / CD max. Max endurance occurs at a CL^3/2 / CD max.
To maximize range for a reciprocating-engine, propeller-driven airplane, we want the following:
1. The largest possible propeller efficiency η.
2. The lowest possible specific fuel consumption c .
3. The highest ratio of W0 / W1 , which is obtained with the largest fuel weight WF .
4. Most importantly, flight at maximum L / D .
Anderson, John. Introduction to Flight (p. 505). McGraw-Hill Higher Education. Kindle Edition.
For a jet airplane, the Breguet Equations are derived from Thrust Required. As such, for jet airplanes CL / CD max corresponds to Max Endurance. Max range occurs at CL^1/2 / CD max.
to obtain maximum range for a jet airplane, we want the following:
1. Minimum thrust-specific fuel consumption ct .
2. Maximum fuel weight Wf .
3. Flight at maximum CL^1/2 / CD
4. Flight at high altitudes
Anderson, John. Introduction to Flight (p. 512). McGraw-Hill Higher Education. Kindle Edition.
I guess you went back for an aero degree after almost orphaning your kid
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