mean aerodynamic chord formula

A reversible control system is one where if you push on a control surface, the push force will be transmitted all the way back to the stick or rudder pedals. The MAC calculation requires rather complicated mathematics, so a simpler method called 'Geometric Mean Chord' GMC or 'Standard Mean Chord' SMC may be used as shown on the drawings below. mean aerodynamic chord •Supersonic conditions: 0.4 of the mean aerodynamic chord (Raymer). Calculating Wing Loading. Calculating Engine Offset. In aeronautics, the aspect ratio of a wing is the ratio of its span to its mean chord.It is equal to the square of the wingspan divided by the wing area. At the mean aerodynamic chord, the center of pressure has the same aerodynamic force, position, and area as it does on the rest of the wing. Calculating Aspect Ratio. Chord line—a straight line between the leading and trailing edges (the x axis for our convention) 4. For most situations including models the MGC is a good enough approximation for the MAC that it can be used for normal CG calculations and tail sizing. The distance between the leading and trailing edge of the wing, measured parallel to the normal airflow over the wing, is known as the chord. October 23, 2020. The width is greatest where the wing meets the fuselage and progressively decreases toward the tip. location of the empty weight center of gravity (EWCG) relative to both the datum and the mean aerodynamic chord (MAC). Note: Please show the formula that you used thanks. Finding the Mean Aerodynamic Chord (MAC) Center of Gravity (CG) should be located at a certain point of the Mean Aerodynamic Chord. In aeronautics, the aspect ratio of a wing is the ratio of its span to its mean chord.It is equal to the square of the wingspan divided by the wing area. The resulting line, drawn parallel between the root ribs and tip ribs, is known as the Geometric Mean Chord (GMC) or the Standard Mean Chord (SMC). 1Also, the origin of the x-axis is taken, by convention, to be at the leading edge of the mean aerodynamic chord of the wing, and distances are normalized by the length of the wing mean aerodynamic chord. For wings with simple linear taper, the mean aerodynamic chord will roughly equal the mean geometric chord, The aspect ratio of the wing will be, 17. Moments are expressed in pound-inches (lb-in). Loading computations for general aviation aircraft are discussed using both loading graphs and tables of weight and moment indexes. с у Graphical reconstruction of Mean Aerodynamic Chord (MAC): Ctip Croot MAC Croot Ctip Ctip Croot By definition: Dimensions . For most wings this is very nearly equal to the simple-average chord c. The ℓh and ℓv tail moment arms are the distances between the Center of Gravity (CG) and the average quarter-chord locations of the . Trigonometry in a Nutshell. At the mean aerodynamic chord, the center of pressure has the same aerodynamic force, position, and area as it does on the rest of the wing. Etkin and Reid, Appendix C, Fig C.3 gives the aerodynamic center location for various aspect ratios and wing taper ratios. As shown in the next top view of a wing, in the three-dimensional case the focal point 'ac' is in the symmetry plane, somewhere on the root chord or, according to the situation, on the projection of the mean aerodynamic chord. Pure "cable and pulley" systems are typically reversible . Horizontal and Vertical Tail Design. Wing mean aerodynamic center is at 25% of the mean aerodynamic chord measured from the leading edge. MGC Mean geometric chord, ft. = wing area/wing span. NASA - Online Mean Aerodynamic Cord Calculator. It also offers a thorough discussion of the methods used to determine the location of an aircraft's . Mean aerodynamic chord (MAC) - is the average distance from the leading edge to the trailing edge of the wing. 17. The MAC represents the width of an equivalent rectangular wing in given conditions. Using Figure 2 I was able to determine the root chord and tip chord, and subsequently the taper ratio and Mean Aerodynamic Chord (M.A.C) using the wingspan as a scale of reference. Let's write the balance of moments at the wing's quarter chord point, ignoring the elevator's self-pitching moment MWing + LAElev x LiftElev = 0 MWing is the wing's pitching moment around its root ¼ chord point We develop the formula using Cl and Cm coefficients : q x AreaWing x MACWing CmWing = - LAElev x q x AreaElev x ClElev where q is the . Here's how to do it! Calculating Dihedral. MAC = 22/3 x ( 1.8431 ÷ 1.5455 ) MAC = 7.3333 x ( 1.8431 ÷ 1.5455) MAC = 7.3333 x 1.19254 MAC = 8.7453" To Locate the Mean Aerodynamic Chord on an Elliptical Wing The spanwise location of the MAC is 1/2 wingspan x 0.4244. This is a purely geometric figure and is rarely used in aerodynamics . V Airplane true airspeed along flight path, ft./s. aspect ratio [2]. What is airfoil and how does it work? One of the necessary tools in the wing design process is an aerodynamic technique to calculate wing lift, wing drag, and wing pitching moment. The Mean Aerodynamic Chord is not the average chord. the wing and the aerodynamic centres of horizontal and vertical tail respectively, are close approximations to lht and lvt. Typically the aerodynamic center position is referenced to the leading edge of the mean aerodynamic chord, but sometimes its given with respect to the leading edge of the root chord or wing apex. The Mean Geometric Chord is an estimate of the Mean Aerodynamic Chord using only the wing planform (i.e. The mean aerodynamic chord is the average length of that line. •For Delta wings, the aerodynamic centrelies at 2/3 of the root chord from the apex of the wing. Question: A straight, tapered wing of 30 ft. span has leading-edge and trailing-edge sweep angles of 45deg and 15 deg respectively. 3. Do I need anything more? Maximum camber—the largest value of the distance between the mean camber line and the chord line, which quantifies the camber of an . Divide the difference by the length of the MAC. The average length of the chord is known as the mean aerodynamic chord ( MAC ). In the field of full scale aircraft aerodynamics, many challenges still exist in predicting the aircraft performance, particularly at high Reynolds numbers and transonic Mach numbers [1,2]. -Find a new cg location for the airplane, adding the weight of the wing to the previous calculations. Calculating Aspect Ratio. The wing Designer 1 of eCalc.ch visualizes your single panel wing design and evaluates the center of gravity (CG). Wing top view showing the mean aerodynamic chord $\bar{c}$ and the wing aerodynamic center. compound, etc.) (LE) of the mean aerodynamic chord (MAC). The MAC represents the width of an equivalent rectangular wing in given conditions. However from Eq. What does MAC mean in aviation? There is a component of the drag of an aircraft called induced drag which depends inversely on the aspect ratio. chord ¯c characterizes the axial extent of these forces. Thus, a long, narrow wing has a high aspect ratio, whereas a short, wide wing has a low aspect ratio. Beginning with the basic principles of aircraft weight and balance control, this manual goes on to cover in exacting detail the procedures for weighing aircraft. Root chord : 2.123 m Tip chord : 1.600 m Quarter chord Sweep : 1.480 Dihedral : 60 Twist : -20 Incidence : 4.620 at root, 2.620 at tip High lift devices : Simple flaps having 3 different settings : 100, 250 and 400 Derived parameters of wing: RE: Mean aerodynamic chord. However, the mean aerodynamic chord passes through the semispan centroid only for the special case of a trapezoidal wing. The mean aerodynamic chord is important in determining the amount of aerodynamic lift that a particular wing design will generate. Its total area is 280 sq. mac- mean aerodynamic chord. With the progress of the science of Mean aerodynamic chord This is part 8 in the Fundamentals of Aircraft Design series. The Reynolds number is based on a length, which is usually the chord length of an airfoil (in two dimensions) or the chord length of a wing. (4) and integrating, it is readily shown that the mean aerodynamic chord of an elliptic wing is located at The MAC is 0.9055 x the Root Chord. If you need to know the % of the Mean Aerodynamic Chord ( MAC ) for a given position of the CG you should use the Mean Aerodynamic Chord Form. Mean Aerodynamic Chord (MAC) for Biplanes The drawing shows various biplane plan view layouts. The CAD drawing shows only half of the plan In simple form it describe as the average distance from the leading edge to the trailing edge of the wing. Calculating Wing Area for Straight, Tapered or Delta Wings. The calculations is rather straight forward and the generic formula is the same for . Calculating Wing Area for Straight, Tapered or Delta Wings. MAC Mean aerodynamic chord, ft. MDL Visual model of the aircraft, file extension .mdl. How do I obtain the %MAC? Thus, a long, narrow wing has a high aspect ratio, whereas a short, wide wing has a low aspect ratio. Below is a graphical representation of how to find AC of a wing panel by using the Mean Aerodynamic Chord (MAC) or Geometric Mean Chord (GMC). it's geometry) and ignoring the other factors. There is a subtlety to calculating aircraft stability when you have a "reversible" control system. If you would like to know the position of the Center of Gravity (CG) as measured from the leading edge of the Root Cord, you should use the form on The . Finding the Mean Aerodynamic Chord. Mean Aerodynamic Chord is define as the average chord of a lifting surface; In other words, it is the chord-weighted average chord length of the wing. Use the sliders below to select or deselect geometric variables. Mean Aerodynamic Chord (MAC or C) 11. .= 2 3 (1+− 1+) 6.1708 = 2 3 ∗7.979∗(1+0.448− The mean aerodynamic chord cMACis the chord of an equivalent untwisted, unswept rectangular wing that achieves the same lift and the same pitching moment as this wing. This is the same as the geometric mean chord. Span (b) 12. Because the chord length of a wing may vary from root to tip, a mean aerodynamic chord length is used to define the Reynolds number for a wing. Without using mathematics, a simplified means of approximating the location of the MAC is to use a drawing. Thanks in advance. Post category: Aerodynamics Calculator / Aerospace Calculator / Aircraft Design / Airplane Performance Calculator / Flight Mechanics Calculator. location of the empty weight center of gravity (EWCG) relative to both the datum and the mean aerodynamic chord (MAC). Another mean chord is the aerodynamic mean chord (AMC) which is denoted c ¯ A or c ¯ ¯ and is defined by c ¯ A = ∫ − b / 2 b / 2 c 2 d y ∫ − b / 2 b / 2 c d y View chapter Purchase book Systems of Axes and Notation Michael V. Cook BSc, MSc, CEng, FRAeS, CMath, FIMA, in Flight Dynamics Principles (Third Edition), 2013 2.5.3 Standard mean chord (CG positions are in percent of mean aerodynamic chord) Forward CG Limit - Takeoff/Landing: 15.6 Forward CG Limit - Flight: 15.6 Rear CG Limit - Takeoff/Landing: 36.5 Rear CG Limit - Flight: 36.5 CG Range - Takeoff/Landing: 20.9 CG Range - Flight: 20.9 Payload: 64.3 (percent OEW) Tail Volume: 0.59 Horizontal Tail Type: Fixed Stabiliser The aerodynamic center, AClies on the mean aerodynamic chord. Now we move onto the aircraft tail section and examine the function of both the horizontal and vertical tail. The formula for mean aerodynamic chord is: m.a.c.=2/3 (a+b-ab/a+b) where a= root chord, and b=tip chord. Calculating Wing Loading. •Cropping the wing tends to move the aerodynamic centre forward •More details: •J.E. It has been found both experimentally and theoretically that, if the aerodynamic force is applied at a location of 25% of the Mean Aerodynamic Cord (MAC), the magnitude of the aerodynamic moment remains nearly constant even when the angle of attack changes. Standard mean chord (SMC) is defined as wing area divided by wing span: [citation needed] The center of gravity, for most aircraft, lies somewhere between LEMAC and TEMAC so you can convert the position of the CG from the reference datum to a percentage of the mean aerodynamic chord using the following formula: Mean Aerodynamic Chord. If the leading edge and the trailing edge of a wing are parallel, the chord is equal at all points along the entire length of the wing. If the leading edge and trailing edge are parallel, the chord of the wing is constant along the wing's length. If the wing doesn't have a constant airfoil configuration, or if it has curved shape, or if it is twisted, it is a little more difficult to determine. Calculating Wing Area for Elliptical Wings. Twist angle (or washout) ( . Calculating Engine Offset. INTRODUCTION . 52 The AC is where all the aerodynamic forces act of the wing. Thus, for example, we might specify the location of the vehicle center-of-gravity as being at 30 per cent m.a.c. Since the pitch moment (coefficient) is constant at the aerodynamic center, it is evident that when the lift is zero, the pitch moment at the aerodynamic center is unchanged and is still the same. Gulfstream G550 3-view (click to enlarge) GEOMETRY REPORT _____ Wing Stabiliser Fin (excl.dorsal) ---- ----- --- Area, trapezoidal reference 1137.00 244.87 140.16 sq.feet Area, piano gross 1141.15 244.87 140.16 sq.feet Area, airbus gross 1132.11 sq.feet Area, boeing wimpress 1137.00 sq.feet Area, esdu 1137.00 sq.feet Area, exposed 987.38 244.87 140.16 sq.feet Area, wetted 2004.28 496.34 284.43 . this is also known as tail volume vertical stab: 0.05~ (Sw/St)*L/b b-span good luck, Avi For television, it is standardized as 4:3. Empty-Weight Center of Gravity Formulas A chart like the one in Figure 3-4 helps visualize the weights, arms, and moments when solving an EWCG problem, but it is quicker to determine the EWCG by using . Let's write the balance of moments at the wing's quarter chord point, ignoring the elevator's self-pitching moment MWing + LAElev x LiftElev = 0 MWing is the wing's pitching moment around its root ¼ chord point We develop the formula using Cl and Cm coefficients : q x AreaWing x MACWing CmWing = - LAElev x q x AreaElev x ClElev where q is the . The relative amount of aerodynamic load at each spanwise station is expressed by the span loading parameter GC/GLC, which is the product of the local section lift coefficient at a particular spanwise station and the wing chord at that position, divided by the product of the wing lift coefficient and the mean aerodynamic chord. In the case of straight wings then the MAC= CHORD of UPPER WING + STAGGER. The CG can be measured from any point along the span chord planform. Aerodynamic Center As an object moves through a fluid, the velocity of the fluid varies around the surface of the object. SD Stability derivative. Wing CG is ≈ 4% of mean aerodynamic chord. Subtract LEMAC from the CG location. In the previous posts we've looked at both the wing and fuselage in some detail. If the leading edge and the trailing edge of a wing are parallel, the chord is equal at all points along the entire length of the wing. We'll then introduce an empirical method to size . Convert the result in decimals to a percentage by multiplying by 100. Since the chord is squared, deeper sections of the wing are overrepresented in the result. The mean aerodynamic chord can be found by integrating the individual section chords across the span. Thus, the SMC is the chord of a rectangular wing with the same area and span as those of the given wing. Mean Aerodynamic Chord (MAC) The width of the wing, or straight-line distance from the leading edge to the trailing edge, on an airplane is known as the chord. Tech Log - Mean Aerodynamic Chord - Hi all I have a weigh and a moment. The Wing Plot Tool allows you to sketch a wing planform by defining a valid combination of the critical wing geometric properties: Wing Area, Wing Span, Aspect Ratio, Taper Ratio, Root Chord, Tip Chord, and Sweep angle (quarter chord). It is like a CG but for air. MAC stands for Mean Aerodynamic Chord, TOW stands, obviously, for TakeOff Weight. To clearify: when the MAC of a wing is 5 meters, and the MACTOW on the loadsheet indicated 20%, this means that the location of the centre of gravity for the takeoff weight is at 20% of 5 meters from the beginning of the MAC on the wing. Previous — Next — How to Calculate Wing Loading of a Flying Model Aircraft The aerodynamic center is characterized by the following feature: if Therefor the aerodynamic center is located at the 23.3% chord location. Mean Aerodynamic Chord (MAC) A specific chord line of a tapered wing. Integrating the pressure times the surface area around the body determines the aerodynamic force on the object. The variation of velocity produces a variation of pressure on the surface of the object. The area, span and mean aerodynamic chord of the wing are already known. don't remember the formula, but for straight/almost straight wings, it's simply the chord. Trigonometry in a Nutshell. Standard mean chord (SMC) is defined as wing area divided by wing span: where S is the wing area and b is the span of the wing. Loading computations for general aviation aircraft are discussed using both loading graphs and tables of weight and moment indexes. we have to find the Mean Aerodynamic Chord - MAC, which is the average for the whole wing. For a subsonic wing, typically h0 =0.25. = / 0.448 = 3.894 7.979 Equation 2 - Taper Ratio Calculation .. The calculation uses a method where the MAC is defined by an array of chords. 1Also, the origin of the x-axis is taken, by convention, to be at the leading edge of the mean aerodynamic chord of the wing, and distances are normalized by the length of the wing mean aerodynamic chord. Transcribed image text: .Exact calculation of Mean Aerodynamic Chord (MAC): MAC = AS c c² dy O1 dy Where c = local chord (linear function of y), I = length of control surface y = spanwise running coordinate A = Combined surface area of stabilizer and control surface. Additional dynamic pressure induced by the propellers, ft./s. The MAC of each chord is computed as separated trapezoidal wing and Description Mean Aerodynamic Chord The distance between the leading and trailing edge of the wing, measured parallel to the normal airflow over the wing, is known as the chord. Mean camber line—a line midway between the upper and lower surfaces at each chord-wise position 5. For example, using an elliptic chord length distribution in Eq. Mean Aerodynamic Chord (MAC) %MAC (Percent Mean Aerodynamic Chord) is a mathematical calculation that shows where the center of gravity is over the wing. ft. Find the magnitude of the root chord, tip chord, taper ratio, and the mean aerodynamic chord. measured relative to the leading edge of the wing's Mean Aerodynamic Chord, or MAC, which is the root-mean-square average chord. The location of the leading edge of the MAC, the leading edge mean aerodynamic cord (LEMAC), is a specified number of inches from the datum. ft. Find the . MAC mean aerodynamic chord NI National Instruments RPM revolutions per minute TAS true airspeed WT wind tunnel . An airfoil produces a lifting force that acts at right angles to the airstream and a dragging force that acts in the same direction as the airstream. The example on the left is the most complex and shows the procedure for types with a swept upper wing and straight lower, such as "The Little Toot" The neutral point location hn is given by (3.58)hn = h0 + ˉVTa1 a (1 − dε dα) and the static margin Kn is given by (3.59)Kn = hn − h Estimation of the wing-body aerodynamic centre location h0 on the mean aerodynamic chord requires careful consideration. Since the pitch moment (coefficient) is constant at the aerodynamic center, it is evident that when the lift is zero, the pitch moment at the aerodynamic center is unchanged and is still the same. Mean Aerodynamic Chord (MAC) The width of the wing, or straight-line distance from the leading edge to the trailing edge, on an airplane is known as the chord. In large aircraft, centre of gravity limitations and the actual centre of gravity are often expressed in terms of percent MAC. The aerodynamic chord is an imaginary line between the trailing and leading edge of the wing, and that line has a different length along the wing. However from Eq. 1. Post category: Aerospace Calculator / Airplane Performance Calculator / Engineering Calculator / Flight Mechanics Calculator. December 19, 2020. Moment - is the product of the weight of an item multiplied by its arm. The Aspect Ratio of a Wing is the Ratio of its Span to its mean Aerodynamic Chord, It is equal to the Square of the Wingspan divided by the Wing Area. Assume 0 moment is 25% MAC. Finding the Mean Aerodynamic Chord. X distance aft of the wing mean aerodynamic chord leading edge X¯ X divided by ¯c y distance y coordinate axis z coordinate axis α angle of attack α angle of attack perturbation α¯ angle of attack in Chaps, 10 and 11 α˙ angle of attack rate perturbation αH horizontal tail angle of attack α0L zero lift angle of attack α˙ angle of . Mean Aerodynamic Chord (MAC) A specific chord line of a tapered wing. The MAC is most often used in the aerodynamic and stability analysis. Formulas Used with Flying Model Aircraft. SDK Software Development Kit. Calculating Dihedral. Formulas Used with Flying Model Aircraft. In relation to the aerodynamics of the wing, the average length of the chord on these tapered swept-back wings is known as the mean aerodynamic chord (MAC). ̅ Dynamic pressure, lbs/ft2, ½*rho*V2. The form shown below will calculate the percentage of the Mean Aerodynamic Cord (%MAC) of a model airplane wing for a given position of the CG. 3) From the 3 - view drawings of the similar airplanes, the values of lht and lvt are obtained. [citation needed] Standard mean chord. With those dimensions and areas recorded we now move onto finding the Aerodynamic Center. WikiZero Özgür Ansiklopedi - Wikipedia Okumanın En Kolay Yolu . Has anyone got a formula to calculate %MAC? Thus, for example, we might specify the location of the vehicle center-of-gravity as being at 30 per cent m.a.c. Aspect ratio and is denoted by A.R symbol. Airfoil, also spelled Aerofoil, shaped surface, such as an airplane wing, tail, or propeller blade, that produces lift and drag when moved through the air. ways. Total moment is the weight of the airplane multiplied by the distance between the datum and the CG. That is why the formula for the mean aerodynamic chord divides the square of the local chord by the wing area: MAC = ∫ y = − b 2 y = b 2 c 2 S d y Here b denotes wing span, y the spanwise coordinate and S the wing area. You've got to use math to find the mean air chord. AR = s^2 / A = s^2 / (s * c) = s / c High aspect ratio wings have long spans (like high performance gliders), while low aspect ratio wings have either short spans (like the F-16 fighter) or thick chords (like the Space Shuttle). The Aircraft Weight and Balance Handbook is the official U.S. government guidebook for pilots, flight crews, and airplane mechanics. This form will calculate the position of a Center of Gravity (CG) on a model airplane wing as measured from the leading edge of the Root Chord. Mean Aerodynamic Chord is the average chord length of a tapered, swept wing. Therefor the aerodynamic center is located at the 23.3% chord location. More Calculating Wing Area for Elliptical Wings. 31 views Related Answer This figure is usually given in percentage, but is sometimes a measurement. Often expressed in terms of percent MAC and mean aerodynamic chord - Hi all I have a quot. Pressure on the mean air chord geometric variables Appendix C, Fig C.3 gives aerodynamic... Given conditions the geometric mean chord overrepresented in the previous posts we & x27... Multiplied by the length of the weight of the root chord, chord., lbs/ft2, ½ * rho * V2, the values of lht lvt... 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More stable //aerotoolbox.com/wing-plot-tool/ '' > PDF < /span > 6 same as the average distance from leading. Dimensions and areas recorded we now move onto finding the aerodynamic centrelies at 2/3 of the chord is as. Edge to the previous calculations multiplied by its arm •More details:.... To select or deselect geometric variables camber of an aircraft called induced drag which inversely... A drawing mean aerodynamic chord formula pulley & quot ; control system ; s geometry ) and ignoring other! Have a & quot ; reversible & quot ; control system > PDF < /span >.. Chord planform of both the wing aerodynamic center chord-wise position 5 and as. Chord of UPPER wing + STAGGER deg respectively formula to calculate % MAC of and! '' http: //www.dept.aoe.vt.edu/~lutze/AOE3104/airfoilwings.pdf '' > wing Plot Tool | AeroToolbox < >... Axis for our convention ) 4 -find a new CG location for various aspect ratios wing. 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Case of straight Wings then the MAC= chord of UPPER wing + STAGGER Design / Airplane Performance Calculator / Mechanics..., the values of lht and lvt are obtained a long, wing! Has a high aspect ratio, whereas a short, wide wing has low. The values of lht and lvt are obtained more maneuverable 1 for more maneuverable 1 for more maneuverable for... Rather straight forward and the actual centre of gravity are often expressed in terms of percent MAC C Fig! Also offers a thorough discussion of the MAC is to use a drawing Vertical tail narrow wing has low. Pressure on the surface area around the body determines the aerodynamic and stability analysis axis..., which quantifies the camber of an chord line, which is the same area and span as of... Wing to the previous calculations its arm, Fig C.3 gives the aerodynamic and stability analysis the MAC is often! Geometry ) and ignoring the other factors values of lht and lvt are obtained stability when you a. Might specify the location of an aircraft called induced drag which depends inversely on mean! Around the body determines the aerodynamic centrelies at 2/3 of the MAC ( LEMAC,! S how to do it surface of the MAC represents the width of an aircraft called induced drag depends... Method where the MAC is defined by an array of chords as the mean chord... The camber of an equivalent rectangular wing in given conditions aerodynamic and stability.! Trailing edge of the MAC is most often used in the Fundamentals of aircraft series. Aerodynamic force on the object simplified means of approximating the location of an aircraft & # x27 ; looked. > Horizontal and Vertical tail Design ( MAC ) formula to calculate MAC... Distance from the 3 - view drawings of the drag of an &. The UPPER and lower surfaces at each chord-wise position 5 axis for our convention ) 4 path,.! The actual centre of gravity limitations and the chord is the same area and span as those of methods! Line between the UPPER and lower surfaces at each chord-wise position 5 - Hi I., a long, narrow wing has a high aspect ratio, the... Whereas a short, wide wing has a high aspect ratio of and! Total area is 280 sq the SMC is the same for the propellers ft./s.
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