CD = Airplane coefficient of drag CL = Airplane coefficient of lift D = Diameter of propeller D50 = Distance from brake release to and aircraft height of 50 feet at sea level conditions.
H = Reference height over the prescribed measurement location HP = Horsepower F = Force (thrust) M = Mach number RC = Rate of climb at V y rpm = Revolutions per minute T = Standard temperature at reference altitude V = Airspeed Vy = Best rate of climb airspeed.
W = Maximum gross takeoff weight = Propeller inflow angle = Pressure ratio at reference height.
γ = Climb angle θ = Temperature ratio at reference height σ = Density ratio at reference height.
Subscripts P = Parent M = Modified R = Rotational A = Airplane TAS = True Airspeed h = Helical tip
(4) Examples of type design changes that may affect noise levels Typical applications for type design changes that require an evaluation of the effect of the change on noise levels include:
a) increase in maximum takeoff weight without any change in engine or propeller installation;
b) change from a fixed pitch propeller to a variable pitch propeller;
c) change in propeller diameter;
d) change in number of blades;
e) increase in engine horsepower; and
f) modification that increases drag without any change in engine or propeller installations. Examples include installation of external cargo containers, larger tires on fixed gear, or advertising light arrays.
In many cases, changes in noise level introduced by these modifications can be determined analytically by using existing data for the unmodified airplane, or by supplementing the existing data with additional performance Page 17
information when that performance is approved by the FAA. If that performance is “equal to” or “better” the applicant CANNOT take credit for “better” performance (e.g ., shorter takeoff distance, increased rate of climb, etc.) when evaluating a modification for acoustical change unless the new performance is subsequently published in an approved Airplane Flight Manual Supplement (AFMS) or Supplemental Airplane Flight Manual (SAFM) for the modification. Most requests for supplemental type certificates (STC) are made by applicants that do not have access to manufacturer's data used to determine noise levels, even if these data exist. Since part 36 Appendix G applies to noise certification tests completed after December 1988, much of the existing fleet of small propeller airplanes do not have noise level data evaluated according to part 36 Appendix G. In order to obtain an STC, an applicant must demonstrate an NAC or conduct an entire Appendix G test. Several examples are given here of ways to substantiate a no acoustical change using the adjustment factors described previously.
There are, however, some design changes which an applicant may propose that Appendix G compliance is not required, based on similarity to previously approved type certificates (TC) or STCs. Examples of this are older airplanes in a series where the series has several diffe rent engine sizes certified in the same basic airframe.
Converting an airplane from one engine power to higher engine power by an applicant for an STC will require the applicant to do a noise analysis, possibly including noise measurements, even though the same engine/airframe combination exists in a production series. The reason for this is that the manufacturer is very unlikely to have demonstrated part 36 Appendix G compliance with any of his production airplanes. Even if the manufacturer has demonstrated compliance and the certificated noise level is published in an FAA Advisory Circular, the data used to demonstrate compliance, including the 90 percent confidence level for the certificated noise level, is proprietary to the manufacturer.
Before the adoption of Appendix G, certain changes to an airplane were accepted as an NAC by the FAA without any analysis. Two examples are the replacement of a two- blade propeller with a three-blade propeller, and an increase of less than 2 percent takeoff weight. For the reasons described below, these two types of changes are no longer accepted as an NAC unless the it is substantiated by analysis and/or test data.
In the case of propeller replacements with increased number of blades, the change in noise generating mechanisms cannot be simply accounted for by tip Mach number and engine power corr ections. Also, the increase in the number of propeller blades shifts the blade passage to higher frequency, which has a smaller A-weighing filter adjustment. In STC applications with propeller changes, the FAA may require a comprehensive NAC analysis to account for the modified noise generation mechanisms, and the A-weighing filter effects or flyover tests have to be conducted.
Increasing the maximum certificated ta keoff weight over the base airplane (or aerodynamic changes which increase drag of the aircraft such that its takeoff performance deteriorates) would cause it to fly at a lower height over the noise measurement location, which results in a higher noise level. An increase in takeoff weight without any change in engine/propeller performance would be an acoustical change unless the noise increase is offset by performance gains or reduction in airplane noise generation, any of which must be substantiated by analysis and/or test data. It is possible to show an NAC condition analy tically as given in Example 1 of this chapter, without actual flight or ground testing.
(4.1) Increase in weight For a change in airplane takeoff weight without any change in engine/propeller installation, the following factors influence the noise level under part 36 Appendix G procedures.
a) As a reasonable first approximation, the takeoff distance to a height of 50 ft (15 m) is increased by a factor equal to the square of the ratio of the weight after the change to the weight before the change.
However, the final determination must be done using the FAA approved takeoff distance from the Approved Airplane Flight Manual (AFM), AFMS, or SAFM.
b) The best-rate-of climb speed will in crease essentially as the square root of the ratio of the weight before and after the change. However, the climb speed (and related performance) in the AFM may not be at the Page 18
best rate of climb speed (Vy) for aircraft type certificated after February 9, 1996. As of this date the climb speed may be dependent on cooling or other airworthiness minimum requirements and not the best rate of climb for the airplane.
c) The climb angle at the incr eased weight will be lower.
The noise level produced at the higher weight will be greater than at the lower weight because these items combine to generate a lower reference height. The increase in airspeed can also cause a modest change in the reference helical tip Mach number, which may increase noise level.
The incremental change in noise level, if nothing else is done, can be shown by an example. Note that the subscript “P” (Parent) is used to denote the "before" conditions and the subscript “M” (Modified) is used to denote the "after" condition.
The following examples are provided to give applicants guidance for NAC analysis. The performance calculations used in the examples are for demonstration purposes only; they are not FAA approved performance calculation procedures. Any change in performance data (takeoff or climb) that is to be utilized in the determination of NAC must be published in the aircraft flight manual.
Example 1: Calculate the change in noise level expected if th e weight of an airplane increases from 3000 lb to 3200 lb, without any other changes, given the following (note that all of the data given is readily available or is calculable from virtually all aircraft operations handbooks):
Step 1 Calculate the parent aircraft reference conditions:
From the AFM/AFMS/SAFM/POH:
D50= 2220 ft Vy = 90 kt RC = 970 ft/min D = 84 in.
rpm= 2600 Calculate:
P = sin -1(RC/Vy) = sin -1[970/(60 × /times 1.688 × 90)] = 6.11° equation (1) HP = tan ( D50) + 50 = tan ( 6.11°) (8200 – 2220) + 50 = 690 ft equation (2) DP = 84 in = propeller diameter rpm = 2600 rpm TP = 59(°F) – lapse rate × H P = 59(°F) – 0.003566 × 690 = 56.5°F equation (3) cP = 49.025 × ( T + 459.67) 1/2 = 1113.8 ft/s equation (4) P= (1 – 0.0000068753 × H P)5.2561 = 0.97532 equation (5) P= ( T+459.67) / (59(°F) + 459.67) = 0.99518 equation (6) P= P/P= 0.98004 equation (7) VTAS = V y / P1/2 = 90.9 knots (True airspeed of parent aircraft) equation (8) MPA = V TAS/cP = 1.688 × 90.9 / 1113.8 = 0.1378 (Mach speed of parent aircraft) equation (9) MPR = D P × rpm × π / (60 × 12 × cP) = 0.8556 (Parent rotational Mach number) equation (10) MPh = (M PA2 + MPR2)1/2 = 0.8666 Page 19
Equation (11) Step 2: Calculate the modified aircraft reference height for a weight of 3200 lb.
a) The takeoff distance before the change, D 50P, is 2220 ft. After the weight increase the takeoff distance is given by:
D50M = 2220 (3200 / 3000)2 = 2526 ft equation (12)
b) The new best rate-of-climb speed at sea level, standard day, V YM, is given by:
VYM = 90 (3200 / 3000)1/2= 93.0 kt equation (13) Note.— This is only a first approximation. Final determination of V Y must be done using FAA approved methods. Unless approved and published in the AFMS/SAFM the applicant must use the V Y value published in the original AFM/POH.
c) Calculating the climb angle at the increased weight can be done by several methods, depending upon the data available from the aircraft operations handbook or flight manual. Where handbook or flight manual data are not available, data such as climb rate or sink rate may be obtained by performing a limited amount of climb tests. Any such performance tests must be conducted with FAA approval.
Method 1:
A general equation for calculating climb performance can be obtained if best rate-of-climb data are available in the aircraft operations handbook for different airplane weights. These data can be used to calculate an effective thrust during takeoff, and the effective ratio of drag to lift. For stable climb conditions at moderate climb angles where the cosine of the climb angle may be assumed to be essentially equal to unity, the sine of the climb angle , which is also the ratio of rate-of-climb to climb speed, is determined from:
sin (= RC / (101.3 × Vy) = F / W – CD / CL equation (14) Note.— The published climb speed in the AFM/AFMS may not be the actual aircraft V y. The applicant is responsible for determining what VY is. See previous note concerning the appropriate speed.
where F is the thrust developed by the propeller, and CD/CL is the ratio of drag to lift coefficients. Thrust is the product of propeller efficiency and engine power, divided by airspeed, with appropriate unit conversions. If it is assumed that the ratio of propeller efficiency to airspeed is approximately constant for airspeeds used for bestrate-of climb, then it can be assumed that thrust remains approximately constant for a given horsepower rating for takeoff. By obtaining RC and V y for two different weights, two simultaneous equations are obtained using equation 14. These may then be solved for F and the ratio of CD/CL, since only the ratio is required.
In addition to the data for a weight of 3000 lb, the flight manual gives a rate-of-climb of 1140 ft/min at 2700 lb.
The best rate-of-climb speed for a weight of 2700 lb will be the speed for 3000 lb times the square root of the ratio of the two weights, or 85.4 kt. Writing two equatio ns with these values, and by subtracting one from the other, the effective thrust, F, is found to be 686 lb, and the drag/lift coefficient ratio is 0.1222.
Substituting the values for thrust, drag/lift ratio, and airspeed for the desired weight of 3200 lb yields climb angle of 5.29°. For a climb airspeed of 93.0 kt, the rate-of-climb is obtained as 868 ft/min.
Method 2:
Rate of climb, RC, in ft/min, is:
RC = (33000 P) / W – RS equation (15) where P is engine horsepower, is propeller efficiency, W is airplane weight in pounds, and Rs is airplane power off sink rate in ft/min.
Some aircraft operations handbooks give a power off glide ratio and speed, from which a sink rate can be calculated. The sink rate calculated using these values is not the same as is obtained when operating at best rateof-climb speed and propeller rpm. The best power off g lide condition for an airplane with a variable pitch propeller is obtained with the propeller at low rpm (i.e., a blade pitch angle that provides minimum drag, and usually at an airspeed that is higher than that for best rate-of-climb). Note that in equation (14), if thrust is zero in glide, then the sine of the glide angle is just equal to the ratio of the drag to lift coefficients. For best glide distance this ratio will be lower than the ratio obtained during takeoff climb. For example, for the airplane in Example 1, the aircraft operations handbook states that the airplane will glide 1.7 nautical miles while losing 1000 ft in height, at an airspeed, V, of 105 knots. The glide angle, g, is calculated by observing that its tangent is given by the ratio of the height lost to the distance traveled. Thus:
g = –tan-1[1000 / (1.7 × 6076.1)] = –5.53° equation (16) In this mode of operation C D/CL is equal to the sine of 5.53°, or 0.0964. In the calculation above, it was found that CD/CL was 0.1222 for takeoff with the propeller operated at maximum rpm.
The rate of sink in takeoff configuration can be obtained by conducting glide tests at the speed for best rate-ofclimb with the propeller at high rpm. The time required to lose a fixed altitude, 1000 ft or more, while holding constant airspeed, will give a sink rate that can be used in equation (15). At 90 kt and high rpm, the sink rate for the example airplane is approximately 1125 ft/m.
Propulsive efficiency, that is the product of propeller efficiency and installed power, can be calculated from equation (15) by using this sink rate, in conjunction with the flight manual value for climb rates at a given weight.
Once these factors have been obtained, the climb rate at a different weight can be calculated, and this, coupled with the new climb speed, will allow the climb angle to be computed as in Example 1.
In Example 1 the best rate-of-climb was 970 ft/min at sea level at a weight of 3000 lb. Substituting these values into equation (15), along with the sink rate of 1125 ft/min, gives a product of propeller efficiency and horsepower, for this airplane, of 190. With no change in horsepower or propeller efficiency, substituting these values in equation (15) gives an equation for rate-of-climb at any weight, W:
RC = (6.285 × 106 / W) – 1125 ft/m At a weight of 3200 lb, the rate-of-climb becomes 839 ft/m. At an airspeed of 93 kt, the climb angle is given by:
= sin-1 [839 / (101.3 × 93)] = 5.11° Method 3:
An empirical expression for calculating the rate-of-climb, RC(2), at one weight, W(2), when the rate-of-climb, RC(1), at a different weight, W(1), is known is given by:
RC(2) = RC(1) [W(1) / W(2)]1.5 equation (17) Substituting 3000 lb for W(1), 3200 lb for W(2), and 970 ft/m for RC(1), RC(2) is calculated to be 880 ft/m. In turn, climb angle by this method is given by:
Page 21
= sin-1 [880 / (101.3 × 93)] = 5.36° Reference height for the 3200 lb takeoff weight can now be calculated with each of the three rate-of-climb values by using the equation:
HM = 50 + (8200 – D50M) × tan ( From the rate-of-climb of Method 1:
HM = 50 + (8200 – 2526) tan (5.29°) = 575 ft From the rate-of-climb of Method 2:
HM = 50 + (8200 – 2526) tan (5.11°) = 557 ft From the rate-of-climb of Method 3:
HM = 50 + (8200 – 2526) tan (5.36°) = 582 ft The modest discrepancies among the three calculated values are related to the erroneous assumption that the ratio of propeller efficiency to airspeed is essentially constant. To be conservative, the lower value for HM may be used in the analysis, or alternatively, the average of the three methods, 571 ft.
Step 2. Calculate reference Mach number.
Speed of sound at height h = 571 ft, from equations (3) and (4) is:
cM = 1114.4 ft/s at 571 ft above sea level
b) Air density ratio at 571 ft is given by equations (5-7):
= 0.97954 / 0.99614 = 0.98334
c) Best rate-of-climb speed of 93.0 kt at se a level becomes true airspeed at 571 ft of:
VTAS = 93 / 0.983341/2 = 93.8 kt
d) Airplane Mach number at 93.8 kt is:
MM = (1.688 × 93.8) / 1114.4 = 0.1421
e) Propeller rotational Mach number is given by equation (10):
MRM = 0.8551
f) Helical tip Mach number is given by the square root of the sum of the squares of the airplane and propeller rotational Mach numbers.
MhM = [(0.1421)2 + (0.8551)2]1/2 = 0.8668 Step 3. Reference horsepower remains essentially constant.
Step 4. Calculate the increment in noise level under part 36 Appendix G operating conditions when the airplane is operated at a weight of 3200 lb instead of at 3000 lb, without further changes.
a) Increase in noise level due to decrease in height from 690 ft to 571 ft:
H = 22 log (690 / 571) = 1.81 dB
b) Increase in noise level due to increase in helical Mach number:
From Example 1, Mh = 0.8666.
M = 150 log (0.8668 / 0.8666) = 0.02 dB Note.— Use of “150” for a “k” factor in the tip mach correction is restricted for use only when the Modified mach number is higher than the Parent mach number. Only an approved “k” determined experimentally for the particular propeller airplane combination may be used when the Modified configuration is lower than the Parent.
c) Change in noise level due to change of inflow angle:
In Example 1 the climb angle (γP) was 6.11° with an assumed pitch angle (P) of 4.25°. Using the average climb angle ( γM) obtained from the three methods described above, 5.25° with an assumed pitch angle (M) of 3.00°. Tests conducted by FAA under controlled conditions in a wind tunnel show that for typical small propeller airplane, sound levels increase as climb angle increases due to the change in air-inflow angle to the propeller. On average an increase of 0.5 dB per degree increase of inflow angle was observed in the tests then, the change due to climb angle is given by = 0.5 (M – P) = 0.5 (3.00° – 4.25°) = –0.63 dB equation (18)
d) Total change in noise level:
The total change in noise level, L, is the algebraic sum of the three adjustments.
L = 1.81 + 0.02 – 0.63 = 1.21 dB Clearly, a substantial acoustical change is created if th e weight for this airplane is increased to 3200 lb without any other change to the engine/ propeller installation or other operating conditions. Once it has been determined that an acoustical change has occurred the applicant must develop new noise levels for the modified airplane. This may mean a full part 36 Appendix G noise test mu st be conducted. If the original data used to determine the aircraft noise levels is available to the applicant then additional adjustments might be made (if within limits) to create new noise levels. The noise levels published in the AFM (if available) CANNOT be adjusted using these calculations.
(4.2) Change from fixed to variable pitch propeller If no other change is made to the airplane, such as increasing horsepower, the primary effect of changing from a fixed to variable pitch propeller of the same diameter is a change in Mach number. Typically, fixed pitch propellers are designed to operate optimally under cruise cond itions where the propeller is designed to reach its maximum continuous rated rpm. During climb at the speed for best rate-of-climb the propeller cannot develop anywhere near its maximum rpm. Typically, takeoff rpm is approximately 85 percent of maximum rpm. For example a 150 hp engine having a maximum propeller rpm of 2700 will develop about 2300 rpm at takeoff. A 235 hp engine with a maximum rated rpm of 2575 typically develops about 2200 rpm in takeoff climb.
One of the primary reasons for changing from a fixed to variable pitch propeller is to shorten takeoff distance and to improve takeoff climb rate. An examination of aircraft operations handbooks for airplanes certified with both fixed and variable pitch propellers, at the same horsepower and takeoff weight, indicates the following nominal characteristics:
a) takeoff distances to a height of 50 ft with variable pitch propellers are approximately 88-90 percent of the distance required with a fixed pitch propeller; and
b) at the same takeoff weight and airspeed, the rate-of-climb with a variable pitch propeller is approximately 9-10 percent greater than with a fixed pitch propeller.
The incremental difference in noise level between an airplane equipped with a variable pitch propeller and a fixed pitch propeller can be estimated by using the same adjustment equations used before for height, Mach number, engine power, and climb angle.
Example 2: The aircraft operations handbook for a representative fixed gear airplane with a takeoff weight of 2900 lb has the following performance data with fixed and variable pitch propellers:
Fixed Variable Takeoff distance, ft 1510 1350 Rate-of-climb, 825 900 ft/min Climb speed, Vy, kt 87 87 Propeller diameter, 80 80 in.
Propeller rpm in 2200 2575 climb Using the equations provided in Section 4.1 above, the following calculated quantities are obtained:
Reference height, ft 679 753 Climb angle, 5.37 5.86 degrees Inflow angle (est.), 5.25 6.15 degrees Speed of sound, ft/s 1113.9 1113.6 True airspeed, kt 87.9 88.0 Airplane Mach 0.1332 0.1334 number Rotational Mach 0.6894 0.8072 number Helical Mach 0.7021 0.8181 number The difference in engine horsepower developed with the two propellers in climb can be calculated by using equation (15) to write two equations for the rate-of-climb in terms of horsepower and sink rate, since the sink rate is the same and thus the only difference in rate-of-climb in the two situations is the actual propulsive power. For the fixed pitch case:
825 = (33000Pf) / 2900 – Rs For the variable pitch case:
900 = (33000Pv) / 2900 – Rs Subtracting the first equation from the second results in a difference of about 7 horsepower. The nominal maximum continuous power for the engine is 235.
All the information necessary to calculate the difference in noise levels between the two propeller installations is now available. The difference in the noise levels for the two cases is the algebraic sum of the following adjustments:
a) Decrease in noise level due to increase in reference height:
H = 22 log (679/753) = –0.99 dB
b) Increase in noise level due to increase in helical Mach number:
M = 150 log (0.8181 / 0.7021) = 9.96 dB
c) Increase in noise level due to increase in engine power:
The rated maximum continuous power for the engine is 235 horsepower. The incremental change in noise level is approximately:
P = 17 log [(235+7)/(235)] = 0.22 dB
d) Increase in noise level due to increase in inflow angle:
= 0.5 × (4.15°–3.25°) = 0.45 dB
e) Total change in noise level:
L = –0.99 + 9.96 + 0.22 + 0.45 = 9.64 dB Clearly, an acoustical change exists between the fixed and variable pitch propeller installations unless some other changes are made to the airplane.
(4.3) Change in propeller diameter Calculating the effect on Appendix G noise level of changing propeller diameter without any other change in power or performance is a straightforward application of the following equation:
M= k log (MM/MP) where k equals a constant dependent on the propeller design and Mach number range. A nominal value of 150 is permitted in G36.201 of part 36 if MP is smaller than MM (Parent and Modified respectively).
Although a change in propeller diameter will usually also change performance, if it can be shown that no degradation in takeoff distance or climb performance is created, the airplane performance before the change can be stipulated as the performance after the change. It is clear that an increase in diameter, considered alone, will increase the noise level. It is sometimes desirable to increase propeller diameter to improve climb performance, sometimes at the sacrifice of some cruise capability. The increased noise level caused by the greater diameter can be offset by a reduction in rpm, if the resulting airplane performance is satisfactory. Where this method is used to show "no acoustical change," it will be necessary to pe rform FAA approved takeoff and climb tests to verify Page 25
performance. The following two examples illustrate the e ffect that changes in propeller diameter have on the noise level.
Example 3: The airplane in Examples 1 and 2 is normally equipped with a two-blade propeller having an 84 inch diameter. The same propulsive efficiency is claimed when using the same engine, same propeller rpm, if the propeller is replaced with a propeller of 86 inches diameter. For the same reference height and airplane speed, the difference in noise level between the two installations ma y be calculated as follows. In Examples 1 and 2, the airplane Mach number was 0.1378 and the propeller rotational Mach number was 0.8556 for an 84 inch diameter propeller. For the same altitude and rpm, the rotational Mach number is directly proportional to the propeller diameter, so the rotational Mach number for the 86 inch diameter propeller is 86/84 times 0.8556, or 0.8760. The corresponding Parent and Modified helical Mach numbers before the change and after the change become 0.8666 and 0.8868. The noise level difference is:
M = 150 log (0.8868 / 0.8666) = 1.50 dB If the new propeller has three blades, which would cause a shift in the blade passage frequency, the above analysis would not be adequate to determine the entire effect of the change. The analysis would have to be extended to account for the noise delta caused by the ground reflections and A-weighing filter effects, or flyover tests would have to be conducted.
Example 4: An applicant wishes to replace an existing variable pitch propeller with a diameter of 76 inches for a different pitched propeller with a diameter of 80 inches. The new propeller is designed to provide a somewhat shorter takeoff distance and better rate-of-climb for the airplane. The applicant does not want to go to the trouble of determining the improvement in takeoff distance or climb rate, and is willing to use the existing handbook data to determine reference height.
The applicant has demonstrated to the FAA that, in flight during reference climb conditions, his existing propeller develops 2600 rpm. He believes that, even with a modest limitation on climb rpm to negate the increase in noise level that a larger diameter propeller would normally generate, the larger propeller will still be advantageous. The rpm limitation that would have to be imposed for "no acoustical change" to result, assuming the reference height of 700 ft and true airspeed of 74 kt do not change and the propeller tip shape and thickness are identical, is determined as follows.
Since the airplane climb speed remains the same, the helical Mach number will be the same if the rotational Mach numbers for the two propellers are held constant. The actual reference height and airspeeds are not relevant to this determination. It is not even necessary to calculate the actual Mach numbers, since the rotational Mach numbers will be the same if the products of propeller diameter and rpm remain constant for the two cases. For the original 76 inch propeller, the product is 76 times 2600 or 197,600. The rpm limitation with an 80 inch propeller is therefore 197,600 divided by 80, or 2470 rpm. If this rpm gives satisfactory takeoff and climb performance, limiting climb rpm to 2470 will result in no acoustical change when the larger propeller is installed. Other airworthiness considerations (e.g., engine cooling, stalling, etc.) may need further consideration.
(4.4) Change in engine power Increasing the size of an engine without changing the takeoff weight of an airplane will change the Appendix G noise level. If no change in performance were involved, the level would increase by 17 times the logarithm of the ratio of the increased horsepower to the original horsepower. However, clearly a change in performance does take place. Takeoff distance is shortened, and climb rate is increased. Often, but not always, a propeller change is also made. If the increase in performance offsets the effect on noise level of the change in engine horsepower, no acoustical change occurs. The following example illustrates the required analysis.
Example 5: The airplane in Example 1 is originally equipped with an engine rated at 225 horsepower at 2600 rpm.
The desired installation is for an engine rated at 250 horsepower at 2650 rpm. The same 84 inch two-blade propeller is used in each case. The acoustical effect of this change is evaluated as follows.
Step 1. If propeller efficiency remains the same, takeoff distance varies inversely with engine power and directly as the square of takeoff weight. The takeoff distance to 50 ft height after the increase in horsepower, D50M, without any weight increase, is the original takeoff distance, D 50P, times the ratio of the original horsepower to the increased horsepower:
D50M = D50P × (HPP/HPM) ft In this example:
D50M = 2220 (225) / (250) = 1998 ft Note.— This is an approximation and the final determination for no acoustical change must use FAA approved data from the AFM or the AFMS for the modified airplane. If the applicant chooses not to take credit for (and thus determine per FAA flight test guidelines) the improved takeoff distance, they cannot take credit for the decrease in distance in the acoustical change determination.
Step 2. From equation (15), rate-of-climb for a given airplane configuration is directly proportional to the ratio of engine power to airplane weight, minus the power off sink rate. The constant of proportionality is the unit conversion factor of 33,000 times the propeller efficiency. In Example 1, the product of propeller horsepower developed in climb is less than the rated horsepower due to installation effects and air density less than at sea level. It can be assumed that the same ratio of losses will apply to a slightly higher rated horsepower engine.
Assuming these losses cancel each other out, the apparent propeller efficiency for Example 1 can be stated as the propulsive efficiency, 190, divided by the rated horsepower, 225, for an apparent efficiency of 0.844. Equation
(15) can then be used to determine the rate-of-climb at the increased horsepower:
RCM = (33000) (0.844) (250) / 3000 – 1125 = 1197 ft/m Step 3. Climb angle is given by:
= sin-1 [RC / (1.688 × 60 × Vy)] M = sin-1[1197/(101.3)(90)] = 7.55° Step 4. The reference height after the change, HM, is:
HM = 50 + (8200–1998) tan (7.55) = 872 ft Step 5. Determine reference helical Mach number:
a) At 872 ft the speed of sound is:
cP = 1113.2 ft/s True airspeed is calibrated airspeed divided by the square root of the density ratio:
P= 0.97472
b) Best rate-of-climb speed of 90 kt at sea level becomes a true airspeed at 872 ft of:
VTAS = 90 / 0.97472 1/2 = 91.2 kt
c) Airplane Mach number at 91.2 kt is:
M = (1.688 × 91.2) / 1113.2 = 0.1383
d) Propeller rotational Mach number is:
MR = 0.8725
e) Helical tip Mach number is:
Mh = [(0.1383)2+ (0.8725)2]1/2 = 0.8834 Step 6. Reference horsepower is now 250.
Step 7. Calculate the increment in noise level under part 36 Appendix G operating conditions:
a) Change in noise level due to increase in height:
From Example 1, HP = 690 ft, and from above HM = 872 ft.
H = 22 log (690 / 872) = –2.24 dB
b) Increase in noise level due to increase in helical Mach number:
From Example 2, Mh = 0.8666:
M = 150 log (0.8834 / 0.8666) = 1.25 dB
c) Increase in noise level due to increase in horsepower:
P = 17 log (250 / 225) = 0.78 dB
d) Change in noise level due to change in inflow angle:
In Example 1 the inflow angle was 6.11 degrees with an assumed inflow angle of 4.25°. From equation
(18):
= 0.5 × (4.25°–3.11°) = 0.57 dB
e) Total change in noise level:
The total change in noise level, L, is the algebraic sum of the four adjustments.
L = –2.24 + 1.25 + 0.78 + 0.57 = 0.36 dB The change in noise level due to an increase in horsepower, in this example, is not offset by the effect of improved takeoff performance, resulting in an "acoustical change" of 0.36 decibel. In order to become an NAC situation, some change in rating should take place. A small reduction in allowable takeoff rpm might be reasonable. Several iterations of the above calculations might be necessary to determine the optimum conditions. Any changes in performance where credit is being claimed must be FAA approved, determined using FAA approved methods, Page 28