I suspected the spreadsheet I have developed was under-predicting rate of climb. To check this, I plugged in values for an RV-7, which should be a known quantity and I hear that Van's performance numbers are not inflated. Sure enough, it is giving me a result of <1,000 fpm and Vmax of 192 mph, whereas the published values are 1,400 fpm and 201 mph. I have been scrubbing my spreadsheet searching for an error for several days, and to double-check this, I plugged the same values into Raymer's spreadsheet and I get similar results.
Let's take one data point (ROC @ 125 mph) as an example and perhaps someone can identify where I have gone astray in the process. The result below is within rounding error of my spreadsheet, so I'm afraid I've probably made a rookie mistake somewhere along the line, but I don't know what it is. I have fiddled with the variables such as CDo, cooling loss, scrubbing drag, etc. to stack the deck in favor of performance, and I still can't seem to get close to Van's published performance. Any insights?
Given:
** Note 2: I am assuming a fixed-pitch metal prop, where efficiency might reach 90% at its design speed. Later we will adjust this downward to account for cooling loss and scrubbing drag when thrust is calculated.
*** Note 3: The published 75% cruise speed is assumed as the prop design speed. Of course, selecting a lower design speed helps rate of climb, but it also reduces Vmax, so I think this is close to a reasonable assumption.
**** Note 4: These cooling loss and scrubbing drag figures are suggested by Raymer. Even if I reduce them to zero, the predicted performance is lower than expected.
Find: Rate of climb at 125 mph (this should be pretty close to Vy).
Solution:
1) Rate of climb Vv = V[(T/W) - 1/(L/D)]
2) V = 125 mph * 5280 ft/mi / 3,600 sec/hr = 183.3 ft/sec
3) To find thrust, we must adjust prop efficiency by several factors: np_adjusted = (np_design)*(np/np_design)*(1-cooling loss)*(1-scrubbing drag)
3a) The fixed-pitch prop adjustment factor, np/np_design, is found based on the prop advance ratio / prop design advace ratio.
3b) Prop advance ratio (design) Jdes = Vdes/(nD) = (191 mi/hr * 5280 ft/mi / 3600 sec/hr) / (2700 rev/min / 60 sec/min * 6 ft) = 1.038 (where n is revs/sec and D is prop diameter in feet).
3c) Prop advance ratio J = V/(nD) = (125 mi/hr * 5280 ft/mi / 3600 sec/hr) / (2700 rev/min / 60 sec/min * 6 ft) = 0.679
3d) J/Jdes = 0.679/1.038 = 0.654
3e) From Simplified p. 95, fig. 60, we find that J/Jdes = 0.65 results in a prop adjustment factor np/np_des = 0.77
3f) Returning to the equation in line (3), np_adjusted = (1.038)(0.679)(0.94)(0.95) = 0.623
3g) Now we can calculate thrust, T = np_adjusted*P/V = (0.623)(160 bhp * 550 ft-lb/sec/hp) / (183.3 ft/sec) = 299 lb
4) The last element we need is L/D, which is equal to CL/CD
4a) CL = (W/S)/q = (1800 lb / 117.4 ft^2)/40 lb/ft^2 = 0.383
4b) CD = CDo+CL^2*K = 0.020646 + (0.383^2 * 0.0676) = 0.031
4c) L/D = CL/CD = 0.383/0.031 = 12.35
5) Finally, plugging all of these values into line (1), we have Vv = V[(T/W) - 1/(L/D)] = 183.3 ft/sec * 60 sec/min * [(299 lb / 1800 lb) - (1/12.35)] = 936 ft/min
Here are the results from my spreadsheet. Any ideas why this is not returning the expected ROC & Vmax?
Let's take one data point (ROC @ 125 mph) as an example and perhaps someone can identify where I have gone astray in the process. The result below is within rounding error of my spreadsheet, so I'm afraid I've probably made a rookie mistake somewhere along the line, but I don't know what it is. I have fiddled with the variables such as CDo, cooling loss, scrubbing drag, etc. to stack the deck in favor of performance, and I still can't seem to get close to Van's published performance. Any insights?
Given:
- Wo = 1,800 lb
- P = 160 bhp
- V = 125 mph (this should be pretty close to Vy)
- rho = 0.00238 slugs/in^3
- q = (0.5)(0.00238)(125*5280/3600)^2 = 40 lb/ft^2
- Aspect ratio A = 5.3
- drag due to lift K = 1/(0.75*pi*A) = 0.0676
- CDo = 0.02065 (*)
- np_design = 0.90 (**)
- prop design speed = 191 mph (***)
- cooling loss = 6% (****)
- scrubbing drag = 5% (****)
** Note 2: I am assuming a fixed-pitch metal prop, where efficiency might reach 90% at its design speed. Later we will adjust this downward to account for cooling loss and scrubbing drag when thrust is calculated.
*** Note 3: The published 75% cruise speed is assumed as the prop design speed. Of course, selecting a lower design speed helps rate of climb, but it also reduces Vmax, so I think this is close to a reasonable assumption.
**** Note 4: These cooling loss and scrubbing drag figures are suggested by Raymer. Even if I reduce them to zero, the predicted performance is lower than expected.
Find: Rate of climb at 125 mph (this should be pretty close to Vy).
Solution:
1) Rate of climb Vv = V[(T/W) - 1/(L/D)]
2) V = 125 mph * 5280 ft/mi / 3,600 sec/hr = 183.3 ft/sec
3) To find thrust, we must adjust prop efficiency by several factors: np_adjusted = (np_design)*(np/np_design)*(1-cooling loss)*(1-scrubbing drag)
3a) The fixed-pitch prop adjustment factor, np/np_design, is found based on the prop advance ratio / prop design advace ratio.
3b) Prop advance ratio (design) Jdes = Vdes/(nD) = (191 mi/hr * 5280 ft/mi / 3600 sec/hr) / (2700 rev/min / 60 sec/min * 6 ft) = 1.038 (where n is revs/sec and D is prop diameter in feet).
3c) Prop advance ratio J = V/(nD) = (125 mi/hr * 5280 ft/mi / 3600 sec/hr) / (2700 rev/min / 60 sec/min * 6 ft) = 0.679
3d) J/Jdes = 0.679/1.038 = 0.654
3e) From Simplified p. 95, fig. 60, we find that J/Jdes = 0.65 results in a prop adjustment factor np/np_des = 0.77
3f) Returning to the equation in line (3), np_adjusted = (1.038)(0.679)(0.94)(0.95) = 0.623
3g) Now we can calculate thrust, T = np_adjusted*P/V = (0.623)(160 bhp * 550 ft-lb/sec/hp) / (183.3 ft/sec) = 299 lb
4) The last element we need is L/D, which is equal to CL/CD
4a) CL = (W/S)/q = (1800 lb / 117.4 ft^2)/40 lb/ft^2 = 0.383
4b) CD = CDo+CL^2*K = 0.020646 + (0.383^2 * 0.0676) = 0.031
4c) L/D = CL/CD = 0.383/0.031 = 12.35
5) Finally, plugging all of these values into line (1), we have Vv = V[(T/W) - 1/(L/D)] = 183.3 ft/sec * 60 sec/min * [(299 lb / 1800 lb) - (1/12.35)] = 936 ft/min
Here are the results from my spreadsheet. Any ideas why this is not returning the expected ROC & Vmax?
