Performance Data for Cessna 411

Using the procedure described above, the five simulated takeoffs (Passes 2 through 6 on Flight Number 411) by definition used an average thrust of 100% of the reference thrust. The six cruise climb configurations (Passes 7 through 11 on Flight Number 411) used an average thrust of 101.1%. The eleven cruise configurations (Passes 12 through 22 on Flight Number 411) used an average thrust of 59.6%. The simulated landings with 10 degrees of flaps (Pass 23 on Flight Number 411 and Passes 1 through 4 on Flight Number 412) averaged 26.6%. Note that Passes 5 and 6 are not included since the power reported on these passes was below the threshold of the power chart as noted in your March 20, 2000 letter. The simulated landings with 30 degrees of flaps (Passes 9 through 11 on Flight Number 412) averaged 58.2%. Table 1 below shows the averages of the parameters used in each of the flight procedures and the resulting percentage of reference thrust. Table 1: Parameters used in the calculation of Percentage of Reference Thrust Flight K n HP KTAS δ F/8 Condition % of Reference Thrust Takeoff Cruise Climb Cruise 10° flaps 325.87 67 325.87 .69 148.3 325.87 .74 325.87 .69 147.2 78.72 .9363 436.0 100 86.63 .9349 441.0 101.1 127.1 117.59 .9357 259.8 59.6 42.1 87.20 .9350 116.0 26.6 approach 30° flaps approach 325.87 .69 102.8 97.77 .9321 253.6 58.2 For modeling purposes, I used the 147.2 HP at the test altitude of 1800 feet MSL and the Lycoming data found in Attachment 2 to calculate a Sea Level power of 155 HP for the MaxTakeoff field in the INM. For the MaxClimb field in the INM, I used data provided by Lycoming to find the approximate power at 3000 feet MSL. I assumed a manifold pressure drop of 1 in. Hg for every 1000 foot increase in altitude and an approximate engine RPM of 2200. The Lycoming Altitude Performance chart, at the intersection of the 2200 RPM line and the 26.8 3 in. Hg line, gives a brake horsepower of approximately140 HP. 2. Aerodynamic Parameters: The INM uses the coefficient of drag divided by lift (R) in the calculation of aircraft climb, cruise, and descent performance. The equation used to find the value of R for various flight conditions is based on equation A12 in SAE AIR 1845: R = F W siny 0.95 where R is the non-dimensional coefficient of drag divided by lift, F is the net thrust in pounds, W is the aircraft weight in pounds, 8 is the non-dimensional pressure ratio, y is the climb angle, and 0.95 is a factor used to correct the climb angle for flight into an assumed headwind. Flaps Zero Climb: Eq. 2 To obtain the climb angle to use with a flaps up (zero degrees), full power takeoff, I used maximum rate of climb data found in Figure 5-6 of the 172R operating handbook (Dec 2/96, Attachment 3) and flight test data. From the figure, I interpolated a rate of climb of 623 FPM at 15°C at 1810 feet pressure altitude (the approximate conditions of the flight test). This climb rate at an airspeed of 80 KTAS (the approximate average true airspeed for passes 2 through 6 on Flight Number 411) corresponds to a climb angle of 4.6 degrees. Using equation 2 above, the calculated Rzero-c value is 0.0831: Y = sin 623 FPM/60 sec/ min 80kt x 1.6878 feet /sec/ kt) = 4.6° F δ R. = zero-c W siny 0.95 2450lb 436.0lb sin(4.6) 0.95 = 0.0831 δ 0.9363 Flaps Ten Climb: To calculate the climb angle to use with a 10° flaps, full power takeoff, I used the short field takeoff distance data found in Figure 5-5 of Attachment 3 and flight test data. For this condition, the aircraft is accelerating while climbing from the lift-off point (end of ground roll) to clearing a 50 foot obstacle. A re-ordered version of SAE-1845 equation A10 was used to determine the R10-c value. For the test conditions, an R10-c value of 0.1446 was found. This higher drag-to-lift ratio than Rzero-c is expected since the short field takeoff technique is not intended to be aerodynamically efficient, but is rather to provide maximum lift at the expense of higher induced drag. The re-ordered version of SAE-1845 equation A10 used to solve for R10-c is the following: 4 R10-C F/8 V₂ = W where F/8 δ V Avg tb S ½ (28) (V₁₂² - V²) A is the net corrected thrust at the average true airspeed in pounds, is the weight in pounds divided by the non-dimensional pressure ratio, Vz/Vavg is the non-dimensional climb gradient, W/8 g Vib Via is the gravitational constant in feet/second², is the final acceleration airspeed in feet/second, is the initial acceleration airspeed in feet/second, and SA is the distance in feet traveled during the acceleration. The values actually used in the calculation of the R10-c are found below. First, the thrust is calculated: KnHp F б V Final S (325.87b-k/HP)(0.67)(147.2HP) (55.8kt)(0.9363) = 615.1lb Eq. 3 where 55.8 KTAS is the average of the 51 knot indicated airspeed (52.7 KTAS, 88.9 feet per second) at the lift-off point of the short field takeoff procedure and the 57 knot indicated airspeed (58.9 KTAS, 99.4 feet per second) at the end of the procedure when obstacles are cleared (50 feet AGL). Both airspeed values are found in Figure 5-5 of Attachment 3. 615.1lb = R10-c 2450lb 50ft ((99.4 ft/sec)² - (88.9 ft/sec)²) 0lb/0.9363 892.3 ft = 0.1446 2 x 32.17 ft/sec² (890.9 ft) The distance of travel in the last term, 890.9 feet, is the difference between the total track distance to clear a 50 foot obstacle and the ground roll distance. Both of these distances are found by interpolating the data in the C-172R short field takeoff distance chart for the test day conditions of 15° C and 1810 feet pressure altitude (Figure 5-5, Attachment 3). For these conditions, the total distance to clear a 50 feet obstacle is 2011.4 feet and the ground roll distance is 1120.5 feet. Also, the climb gradient term, 50 ft/892.3 ft, is the height of the aircraft above the ground (the obstacle height) divided by the total distance which the aircraft travels once it leaves the ground. This total distance is the hypotenuse of a right triangle that has the 50 foot obstacle height and the 890.9 total track distance as the other two sides. Flaps Zero Cruise: In cruise configuration, Rcruise was found from the data in Figure 5-8, Cruise Performance (Attachment 3). For standard temperature conditions, Rcruise varies from 0.100 to 0.122 depending on altitude and power setting, where the altitudes of interest are from 4000 feet to 8000 feet. For the listed power settings, the average Rcruise was 0.096. This corresponds to power settings of about 70%. The following equation and Table 2 below shows how the data from Attachment 3 5 was used to generate the Renuise values. For the horsepower term in the thrust equation, the percentage power is multiplied by the 160 HP rating of the Lycoming IO-360-L2A. sin(0) (325.87) (0.74)(160 HP) (% HP/100) F F δ siny δ Rcruise W 0.95 W 0.95 δ (2450lb)KTAS Table 2: Cruise Performance Altitude Engine RPM % HP KIAS KTAS Rcruise (feet) 4000 2300 79 110 117 .106 2250 75 107 114 .104 2200 70 105 111 .099 2100 62 99 105 .093 2000 55 92 98 .089 1900 50 85 90 .087 6000 2350 80 110 120 .105 2300 75 107 117 .101 2250 71 104 114 .098 2200 67 101 111 .095 2100 60 95 104 .090 2000 53 88 96 .087 8000 2400 80 108 122 .104 2350 76 106 119 .101 2300 71 103 116 .097 2200 64 98 110 .091 2100 57 90 102 .088 2000 52 83 94 .087 Average: 0.096 6 Approach Flaps: Equations 1 and 2 were used to determine the R values for approach conditions. As seen in Table 1, during the 10 degree flaps approach, the power averaged 42.1 HP, and the airspeed averaged 87.2 KTAS, for a net corrected thrust of 132.3 lb. During the 30 degree flaps approaches, the power averaged 102.8 HP, and the airspeed averaged 97.8 KTAS. For these approaches, the flight path of the aircraft was determined from the video data taken during the flight test. The nominal flight path was 3 degrees down for both series of approaches. Using these data, RD-10 was found to be 0.0994, while RD-30 was found to be 0.1516. Note that the approaches flown at relatively high power, 85 KIAS, and 30 degree of flaps were not used, since Cessna personnel stated that these were non-standard approach conditions. F/ siny 116.0lb RD-10 = W 0.95 2450lb sin(-3.0) 0.95 = : 0.0994 δ 0.9350 siny 253.6lb 0.95 2450lb sin(-3.0) 0.95 = 0.1516 δ 0.9321 Rp-30 = F/8 W Takeoff Roll Distance: The INM takeoff roll distance coefficient B was found using SAE AIR 1845 equation A6 and assuming Sea Level ISA conditions. The ground roll with 10 degrees of flaps was taken directly from the short field takeoff distance chart (Figure 5-5, Attachment 3). The initial climb speed for the 10 degrees flaps takeoff was listed in this figure as 51 KTAS (86.08 feet per second). For the zero flaps takeoff, the ground roll was calculated assuming a rotation speed of 55 KTAS (92.83 feet per second) as listed in the normal takeoff procedures section of the operators handbook (Page 4-14, Attachment 4). The following equations show the computation of the additional distance required to accelerate to this higher speed. F KnHp δ Vavg8 (325.87b/HP)(0.67)(147.2HP) (53kt)(1.0) = 606.4lb SA ½ (0.95) (V-V2) ½/2x32.17 (0.95)(92.83² - 86.08²) tb F δ R δ W 606.4 0.0831 2450/ 1.0 = = 108.5 feet For the zero flap takeoff, the 108.5 foot distance is added to the 945 foot interpolated short field distance to give a total takeoff ground roll distance of 1053.5 feet. For Sea Level ISA conditions, the final thrust used in the calculation of the INM's zero flaps B coefficient, B, is based on the reference thrust applied at the lift-off speed of 55 KTAS. F δ KnHp V Final Final (325.87bk/HP)(0.67)(147.2HP) (55kt)(1.0) = 584lb 7 δ B₂ $(F/S) 1053.5ft x 584lb = = 0.1025 W2 (24501b)² Eq. 4 For the ten degree flaps takeoff, the 945 foot interpolated short field distance is used as the take- off ground roll in the computation of the B10 coefficient. The final thrust for this condition is the reference thrust applied at the lift-off speed of 51 knots (Figure 5-5, Attachment 3). F б B10 = KnHp V Final S $(F/S) W² (325.87b/HP)(0.67)(147.2HP) (51kt)(1.0) == 630lb 945ft x 630lb (2450lb)² = 0.0992 Lift-off and Touch-down speeds: The SAE-AIR-1845 equations used to set the lift-off and the touch-down speed coefficients are only a function of weight and the appropriate speed. The lift-off speed coefficient C is defined in SAE-AIR-1845 equation A7. The touch-down speed coefficient D is defined in SAE-AIR-1845 equation A13. The subscripts on the coefficients indicate the flap setting. Lift-off speeds have been discussed in previous sections of this letter report. Touch-down speeds are taken from page 4-16 of Attachment 4. V Cz √W 55kts √24501b = 1.1112 V 51kts = 1.0304 √W √2450lb V 65kts = = 1.3132 С10 D10 D 30 = √W √2450lb V 62kts 1.2526 √W √24501b 3. Modeling Takeoff and Approach in the INM: Eq. 5 Using the performance coefficients described above, I have entered a takeoff procedure and an approach procedure into the INM. The takeoff procedure is a normal takeoff, as described in the Normal Procedures section of the 172R Operators Handbook (Attachments 3 and 4). The approach procedure is a normal approach, as described in the Normal Procedures section. In general, when the Operators Handbook lists a range of speeds for a particular operation, I selected the midpoint of the range of speeds. In addition, graphs of the INM's calculated 8 approach procedure is a normal approach, as described in the Normal Procedures section. In general, when the Operators Handbook lists a range of speeds for a particular operation, I selected the midpoint of the range of speeds. In addition, graphs of the INM's calculated performance profiles for these operations are included. Normal Takeoff: The normal takeoff procedure for the Cessna 172R is detailed page 4-14 of Attachment 4. Flaps are assumed to be retracted throughout the procedure. The aircraft is rotated at 55 KIAS, then accelerates to a climb speed of 75 KIAS. The aircraft climbs at this speed until reaching 1000 Feet AGL, at which point the aircraft is accelerated to an en route climb speed of 80 KIAS (Enroute Climb, Page 4-15, Attachment 4). The aircraft climbs to an altitude of 8000 feet at this speed. The operators handbook recommends a full power en route climb. At three thousand feet, the engine power is changed from MaxTakeOff to MaxClimb. This change in modeled engine power takes into account the decrease in engine power with altitude. This modeled two-step change in power with altitude is an approximation of the true engine power change which is a continually varying function of altitude. Normal Approach: The normal landing procedure for the Cessna 172R is generally described in Attachment 3 on page 4-16. The aircraft begins the landing approach at 100 KIAS, 6000 feet AGL and a three degree glideslope. At 4000 feet AGL, the aircraft begins deceleration to 80 KIAS. At 1000 feet AGL, 10 degrees of flaps are applied. Between 600 and 500 feet AGL the aircraft decelerates to 70 KIAS. The aircraft touches down at 62 KIAS, and rolls 560 feet. In addition to the normal takeoff and approach, data generated in this report is sufficient to generate non-standard takeoff and approach procedures. These procedures are not included here because they are subject to airport-specific variations. Graphs showing altitude, true airspeed, and net corrected thrust for the three procedures listed above are presented on the following pages. The independent axis for the takeoff procedures is the distance from brake release; for approach, the independent axis is the distance from touchdown (negative before touchdown, positive after touchdown). The graphs assume standard temperature and a sea level airport. In addition, the NPD data are also included in this letter report in tabular form. ACOUSTICS FACILITY Drand Sony David Senzig, P.E. C: John Gulding, FAA 9 Summary of INM Data STUDY AIRCRAFT C-172 User-defined Descrip : Cessna 172R / Lycoming IO-360-L2A : GA UserID WgtCat : Small OwnerCat Gen-Aviation EngType : Piston NoiseCat 9855388 Type : Prop NumEng : 1 NoiseId : ATRS TkoWgt LndWgt : No 2450 lb : 2450 lb LndDist : 1695 ft StaticThr : 536 lb GASEPF Standard data USER-DEFINED PROFILE IDENTIFIERS Op C-172 APP STANDARD 1 DEP STANDARD 1 Profile Stg Weight (lb) 2450 2450 USER-DEFINED PROCEDURAL PROFILES # StepType Flap ThrType Alt/clm Speed (kt) Ang/Thr/Dis C-172-APP-STANDARD-1 1 Descend ZERO-D None 6000.0 ft 100.0 3.0 deg 2 Descend ZERO-D None 4000.0 ft 100.0 3.0 deg 3 Descend ZERO-D None 3000.0 ft 80.0 3.0 deg 4 Descend 10-D None 1000.0 ft 80.0 3.0 deg 5 Descend 10-D None 600.0 ft 80.0 3.0 deg 6 Descend 10-D None 500.0 ft 70.0 3.0 deg 7 Land 10-D None 30.0 ft 0.0 0.0 8 Decelerate 10-D None 530.0 ft 62.0 10.0 % 9 Decelerate -NONE- None 0.0 ft 10.0 10.0 % C-172-DEP-STANDARD-1 1 Takeoff 2 Accelerate 3 Climb 4 Accelerate 5 Climb 6 Climb 7 Climb ZERO-C MaxTakeOff ZERO-C MaxTakeOff ZERO-C MaxTakeOff ZERO-C MaxTakeOff ZERO-C MaxClimb ZERO-C MaxClimb ZERO-C MaxClimb 0.0 0.0 0.0 500.0 fpm 75.0 0.0 1000.0 ft 0.0 0.0 500.0 fpm 80.0 0.0 3000.0 ft 0.0 0.0 5000.0 ft 0.0 0.0 8000.0 ft 0.0 0.0 Summary of INM Coefficients ACFT OP FLAP C-172 D 10-C COEFF R 0.144600 COEFF CD COEFF B 1.030400 0.099200 C-172 C-172 A 30-D A 10-D 0.099400 1.313200 0.000000 0.151600 1.252600 0.000000 C-172 D CRUISE 0.096000 0.000000 0.000000 C-172 D ZERO-C 0.083100 1. 111200 0.102500 10 Altitude (feet) 8000- 6000 4000 2000 Cessna 172R Standard Takeoff Modeled Altitude Profile 0 0 20000 40000 60000 Distance (feet) 80000 100000 120000 C:\Projects\Cessna\Basecase\prof_pts.qpw 08/29/00 100 90 90 80 80 50 True Airspeed (knots) 50 60 60 70 40 40 30 30 Cessna 172R Standard Takeoff Modeled Speed Profile ☐ 0 20000 40000 C:\Projects\Cessna\Basecase\prof_pts.qpw 60000 Distance (feet) 08/29/00 80000 100000 120000 150 140 130 120 Net Corrected Thrust (percent) 110 100 90 90 + Cessna 172R Standard Takeoff Modeled Thrust Profile 20000 40000 60000 Distance (feet) 80000 100000 120000 C:\Projects\Cessna\Basecase\prof_pts.qpw 08/29/00 Altitude (feet) 6000 5000 4000 3000 2000 1000 Cessna 172R Standard Approach Modeled Altitude Profile -120000 -100000 -80000 -60000 -40000 Distance (feet) -20000 0 20000 C:\Projects\Cessna\Basecase\prof_pts.qpw 08/29/00 110 100 True Airspeed (knots) 90 90 60 80 70 Cessna 172R Standard Approach Modeled Airspeed Profile 60 -120000 -100000 -80000 -60000 -40000 -20000 Distance (feet) C:\Projects\Cessna\Basecase\prof_pts.qpw 08/29/00 。 0 20000