27Ouhib U73349256Boeing 737-700 Drag Project(Without Winglets)

EAS 4121 Spring 2014Abdel Ouhib

U73349256

Table of ContentsIntroduction....................................................................................................................................1Calculations.....................................................................................................................................4Parasitic Drag..................................................................................................................................4Interference/Other Drag...............................................................................................................11Induced Drag.................................................................................................................................12Compressibility Drag.....................................................................................................................15Total Drag.....................................................................................................................................17Results..........................................................................................................................................18Appendix.......................................................................................................................................19References....................................................................................................................................27

Introduction

The Boeing Company is one of the most respected and sought-after names in the aeronautical industry today. Boeing has achieved this status by designing and manufacturing some of the worlds most reliable and efficient aircraft. In the fleet of the Boeing Company is the 737 subsonic jetliner. The 737 was originally nicknamed the square jet, because the length of the aircraft was nearly equivalent to the length of the wingspan. At the time of design, which began in 1967, Boeing was in competition with the British Aerospace Company, as well as the Douglas Aircraft Company. The Boeing engineers and designers needed to design the 737 to remain competitive and a leader in the aeronautical industry.Prior to the 737, Boeing had released the 707 and 727. The major additions that the company made to these aircraft to create the 737 were the placement of the engines on the wing, as well as the alteration of the cabin to allow a larger seating capacity. The changes made to the position of the engine beneath the wing allowed for some noise buffering, as well as a reduction in vibration, and easier maintenance at ground level. Boeings 737 managed to seat more passengers than the competing DC-9, making it the more attractive aircraft. By 1987, Boeing had managed to make the 737 the most ordered plane in commercial history. The 737-700 is capable of seating between 126 and 149, and uses CFM56 turbofan engines. These engines, featured on the Next Generation 737 aircraft (600-900) are more fuel-efficient and provide a reduction of noise when compared to the Pratt & Whitney JT8D engines used on the classic series (300-500). The first 737-700 was launched in November of 1993. This report will analyze the total drag force that is experienced by a 737-700 at cruise. The drag components that will be analyzed will be the induced drag, interference drag, the compressibility drag, and the parasitic drag. Each of these components will be calculated separately, and combined at the end of the report to solve for the total drag experienced, as well as the lift to drag ratio. The parasitic drag component will be separated into several different parts to account for the total parasitic drag. These components will include the wing, fuselage, horizontal stabilizer, vertical fin, nacelles, and pylons. Landing gear will not be included, as the aircraft is at cruise. The aircraft will be analyzed at its typical cruise Mach and height. Figure 1 displays the typical standard day data that this project will analyze the aircraft at.

Figure 1 (Standard Day Values)

Figure 2 shows the dimensions necessary for calculating the total drag on the aircraft. Several of these values were estimated from AutoCAD drawings provided by Boeing. Other values were obtained from www.b737.org.uk/techspecsdetailed.htm. The specs from this website were compared and checked with the AutoCAD drawings.

Figure 2 (Dimensions of Aircraft)

Several estimations in these dimensions were used. For the fuselage wetted area, the nose and tapered tail were taken into account to solve for the wetted area. The tail and nose were treated as cones to solve for a closer value to the wetted area of the fuselage. These incorporations led to a reduction of the wetted area by 20%. The thickness values, as well as the thickness/root chord values were also estimated. Using the AutoCAD drawings provided, and applying Equation 1 taken from Fundamentals of Flight by Richard S. Shevell, the average thicknesses as well as thicknesses/root chords were obtained for wing, vertical fin, and horizontal stabilizer. (Equation 1)

Where and are root thickness and tip thickness, respectively, and and are root chord and tip chord, respectively. These values are based on a linear thickness. The 737-700 however, is nonlinear, which results in approximated values. The vertical fin exposed area was also approximated, treating the fin as a triangular surface with a certain thickness. The surface area can then be approximated by use of simple triangle and rectangle geometry. The wing area covered by the fuselage was also approximated. This value was approximated by using the AutoCAD drawings to find the diameter of the fuselage, and the length of the root chord of the wing. The wing covered roughly half the circumference of the fuselage. Treating the fuselage as a cylinder, the cross sectional area of the wing covering the cylinder can then be calculated. This same procedure was used for the nacelles as well.

Once the dimensions and thermophysical properties for a standard day and altitude were obtained, the calculations for drag were able to begin.

CalculationsParasitic Drag

Using the values from Figure 1 and Figure 2, as well as several charts within Shevells book, the parasitic drag calculations for the wing, fuselage, horizontal stabilizer, vertical fin, and nacelles could be calculated.

WingIn finding the parasitic drag, the first step is to calculate the Reynolds number. This equation can be referenced as Equation 2.

(Equation 2)

Where v is the velocity in ft/s, L is the Mean Aerodynamic Chord in ft, and is the kinematic viscosity in ft2/s. If the Mean Aerodynamic Chord is not given, but a taper ratio is, Equation 3 can be referenced to solve for the Mean Aerodynamic Chord.

(Equation 3)

Where Cr is the root chord at the centerline of the wing or the side of the fuselage, and is the taper ratio. For the wing, the mean aerodynamic chord is given, so Equation 3 will not be necessary for this component.

Solving for the Reynolds number from Equation 2:

With the Reynolds number and Figure 11.2 in Fundamentals of Flight (pg. 179), a skin friction coefficient can be estimated. A skin friction coefficient, Cf, was estimated to be 0.00275. Knowing the sweepback angle of the wing, as well as the thickness/chord (t/c), it is possible to find the correction factor k from Figure 11.3 in Fundamentals of Flight (pg. 182). Using the data obtained, and an estimation, a form factor, k, was estimated at 1.31. With these values, and reference to Equation 4, a coefficient of parasitic drag for the wing can be calculated.

(Equation 4)

Where Sref is the wing planform area. The remaining values were found in the previous paragraph. Applying values:

This is the result for the parasitic drag coefficient for the wing, which is unitless. An excel diagram with the calculations and values can be referenced in Figure 3.

Figure 3 (Parasitic Drag Coefficient for Wing)

FuselageSimilar to the wing, the same steps are taken to find the parasitic drag coefficient for the fuselage. The first step is to use Equation 2 to solve for the Reynolds Number.

Using the Reynolds number and Figure 11.2 in Fundamentals of Flight (pg.179), a skin friction coefficient can be estimated. The skin friction coefficient, Cf, was estimated to be 0.0021. Using Figure 11.4 in in Fundamentals of Flight (pg.183), a body form factor, k, can be attributed to the fuselage. A fineness ratio must first be calculated. Equation 5 refers to the equation used to calculate a fineness ratio.

(Equation 5)

Where L is the root chord or length of the component, and D is the outside diameter. Applying numerical values to Equation 5:

Using the values of the fineness ratio, a body form factor of 1.15 was estimated. This value may be skewed because the chart used assumed a Mach number of 0.5. Using the values found from charts and Equation 6, a coefficient of parasitic drag for the fuselage can be calculated.

(Equation 6)

Substituting values, a numerical value is obtained:

= 0.005747594

This is the result for the parasitic drag coefficient for the fuselage, which is unitless. An excel diagram with the calculations and values can be referenced in Figure 4.

Figure 4 (Parasitic Drag for Fuselage)

Horizontal StabilizerFinding the coefficient of parasitic drag for the horizontal stabilizer contains similar steps as the previous two components, except the use of Equation 3 is necessary to find the mean aerodynamic chord. Using the taper ratio and root chord values, the mean aerodynamic chord can be calculated.

ft

Using the mean aerodynamic chord, and using Equation 2, the Reynolds number can be calculated.

Using the Reynolds number and Figure 11.2 in Fundamentals of Flight (pg.179), a skin friction coefficient can be estimated. A skin friction coefficient for the horizontal stabilizer, Cf, was estimated to be 0.003. With the given sweepback, and estimated t/c, a form factor, k, can be estimated. A form factor was estimated to be about 1.19. Using this data, the coefficient of parasitic drag for the horizontal stabilizer can be calculated using Equation 7.

(Equation 7)

Substituting values into Equation 7, a numerical value can be obtained.

Although a wetted area is not provided for the horizontal stabilizer, the wetted area can be represented as twice the surface area in contact with the air, and increased by a factor of 1.02 to correct for curvature. Figure 5 is a diagram with the calculations and values for the parasitic drag for the horizontal stabilizer.

Figure 5 (Parasitic Drag for Horizontal Stabilizer)

Vertical FinSimilar to the horizontal stabilizer, the mean aerodynamic chord must be calculated for the vertical fin. Using Equation 3:

Using the mean aerodynamic chord, and using Equation 2, the Reynolds number can be calculated.

Using the Reynolds number and Figure 11.2 in Fundamentals of Flight (pg.179), a skin friction coefficient can be estimated. A skin friction coefficient for the vertical fin, Cf, was estimated to be 0.00275. With the given sweepback, and estimated t/c, a form factor, k, can be estimated. I estimated the form factor to be about 1.09. Using this data, the coefficient of parasitic drag for the horizontal stabilizer can be calculated using Equation 8.

(Equation 8)

Substituting in numerical vales:

Figure 6 is a chart with the calculations and values for the parasitic drag on the vertical fin.

Figure 6 (Parasitic drag on vertical fin)

NacellesThe nacelle calculation for parasitic drag is a little more involved. The mean aerodynamic chord is given as the length, which can be retrieved from the AutoCAD drawings provided. However, the diameters of the nacelles on this aircraft are more complicated. Because they are not perfectly circular, the maximum diameter of the power plant, the CFM56-7B, was used to find the fineness ratio. The diameter of the engines is 61 inches, or 5.08 ft. Using this, a fineness ratio can be calculated by referring to Equation 5.

Referring to figure 11.4 in Fundamentals of Flight, it becomes apparent that extrapolation is necessary to solve for the body form factor, k. To do this, I used two different methods to converge on a final result. The first method was linear extrapolation. The equation for linear extrapolation can be referenced in Equation 9. I then used Microsoft Excel to plot figure 11.4, and add a polynomial trendline. I used this trendline to solve for my body form factor corresponding to the fineness ratio of 3.12. Figure 7 shows the plot and trendline.

(Equation 9)

Where Kn1FR is the first known fineness ratio on the chart, Cor1K is the corresponding body form factor to the first known fineness ratio, Kn2Fr is the second known fineness ratio, and Cor2K is the second corresponding body form factor. K and 3.12 are the values corresponding to the aircraft. Applying values to Equation 9:

Figure 7

Using the equation for the trendline, and an x value of 3.12, a body form factor of 1.46 is achieved. The two values from the two methods are relatively close. Calculating an average of the two body form factors; a final body form factor of 1.485 will be used. Finding a Reynolds number using Equation 2 is necessary to fin the skin friction factor.

A corresponding skin friction factor to the Reynolds number was estimated to be 0.00275. Using the skin friction factor, the body form factor, the wetted area, the reference area, and Equation 10, a coefficient of parasitic drag for the nacelles can be calculated.(Equation 10)

The 2 in the numerator of Equation 10 accounts for two nacelles on the aircraft. Applying values:

Figure 8 includes a chart with the calculations through Microsoft Excel.

Figure 8 (Parasitic drag on nacelles)

PylonsThe pylons on the aircraft are also accounted for in parasitic drag. The root chord can be found from the AutoCAD drawings provided. The length was about 15 feet. Using this value, and Equation 2, a Reynolds number can be calculated.

With the Reynolds number, and assuming typical transport aircraft roughness, a skin friction factor of 0.0027 can be estimated. The pylons on the aircraft have a sweep of zero. Using the sweepback value, and the thickness/chord, a form factor can be calculated. Using Figure 11.3 out of Fundamentals of Flight, a form factor of 1.14 was estimated. Using these values, a coefficient of parasitic drag on the pylons can be calculated using Equation 11. Note: the 2 in the numerator of the equation accounts for both pylons.

(Equation 11)

Applying values to Equation 11:

Figure 9 shows the data calculations using Microsoft Excel.

Figure 9 (Coefficient of Parasitic Drag for Pylons)

The total parasitic drag coefficient is the summation of each of the coefficient of parasitic drag values for each component on the aircraft. When the summation is taken for the wing, fuselage, horizontal stabilizer, vertical fin, nacelles, and pylons, a total coefficient of parasitic drag is calculated to be: 0.0177.

Interference/Other

From knowing the coefficient of parasitic drag on the aircraft, estimation for interference/other drag can be calculated. Interference drag can be caused by a number of factors, including higher induced velocities, and aircraft design. The proper use of fillets on the aircraft can help reduce interference drag on the aircraft. Common areas for interference drag include the connection of the wing to the fuselage, the horizontal stabilizer, or pylons. Any component connected to the aircraft that increases parasitic drag will increase the interference drag.

To account for interference drag, a percentage of the parasitic drag will be added. Because this project is analyzing the aircraft at cruise, the aircraft can be considered to have sealed surfaces. According to Fundamentals of Flight, for a turbine powered aircraft with sealed control surfaces, 6% of the total parasitic drag can be attributed to interference drag. Given that the parasitic drag coefficient is 0.0177, 6% is 0.01062. Therefor, the coefficient of interference drag on the aircraft is: 0.00106. An excel diagram can be seen calculating these values in Figure 10.

Figure 10 (Coefficient of Interference Drag)

Induced Drag

The next step to finding the total drag on the aircraft is to consider the drag due to lift on the wing. In order to do so, Equation 12 will be used, where CL is the coefficient of lift, AR is the aspect ratio, and e is the efficiency factor. There will be several intermediate steps before calculating the induced drag.

(Equation 12)

There are two unknowns in Equation 12 that must be calculated. These are CL and e. To find the coefficient of lift, Equation 13 can be utilized, where W is the weight in lbs, is the density in slugs/ft^3, S is the wing planform area in ft^2, and V is the velocity in ft/s. These values can be referenced from Figures 1 and 2.

(Equation 13)

Applying values to Equation13:

The next step to solve for the induced drag is to calculate the efficiency factor, e. There are two methods to calculating the efficiency factor. It is possible to use Figure 11 referenced from in Fundamentals of Flight with Equation 14 referenced from Fundamentals of Flight to calculate the efficiency factor, e.

(Equation 14)

Figure 11

Using the fuselage diameter divided by the wingspan, a value for s can be found and used in Equation 14. In Equation 14, AR is the aspect ratio of the aircraft, k is the correction factor, s is the induced drag factor, and u is assumed to be 0.99. Applying these values to Equation 14:

The aspect ratio can be referenced as the wingspan squared divided by the exposed planform area. The body form factor can be calculated as 0.417 multiplied by the coefficient of parasitic drag. The value 0.417 was calculated using interpolation. From Fundamentals of Flight, average values of k are calculated at 0.38 multiplied by the coefficient of parasitic drag for unswept wings. For wings at 20, the coefficient of parasitic drag is multiplied by 0.4. For wings at 35, the coefficient of parasitic drag is multiplied by 0.45. Interpolating to find the value to multiply by the coefficient of parasitic drag, a value of 0.417 is obtained for wings swept at 25. S can be seen from Figure 11, using the fuselage diameter divided by the wingspan. The raw data can be referenced in Figure 2.

Another method for calculating the efficiency factor is using Figure 11.8 out of Fundamentals of Flight. Knowing the aspect ratio and the coefficient of parasitic drag, estimation can be made from the chart given in the textbook. For simplicity, this figure can be referenced in Figure 12.

Figure 12

Using figure 12, with an aspect ratio of 9.45 and a coefficient of parasitic drag of 0.0177, an aircraft efficiency factor can be estimated to be 0.81.

Taking the average of the calculated efficiency factor of 0.796 and the estimated efficiency factor at 0.81, an efficiency factor of 0.803 will be used to calculate the induced drag on the aircraft. Inserting values into Equation 12, a coefficient of induced drag is calculated.

This value is the coefficient of induced drag. An excel program displayed in Figure 13 with the above calculations for induced drag.

Figure 13 (Induced Drag Coefficient Calculation)

Compressibility Drag

Because the aircraft is not flying at Mach 0.3 or below, the calculations must include compressibility to be considered accurate. There are several intermediate steps that need to be taken before arriving at a final coefficient of drag due to compressibility. The first step is finding the Mcc=0. This value can be obtained by knowing the thickness/chord, assuming a sweep of 0 degrees, the coefficient of lift, and using Figure 12.7 in Fundamentals of Flight. This value was estimated to be 0.66.

The next step taken was to find the coefficient m used in Equation 15. To find the exponent m, Figure 12.9 in Fundamentals of Flight and the coefficient of lift on the aircraft can be used. With these values, an exponent m was found to be 0.57. Using these values, Equation 14 can be solved to find the critical crest Mach number at the sweep. is the sweep, and can be referenced from Figure 2. Note: calculations should be in degrees.

(Equation 15)

Substituting values into Equation 14:

It is then possible to compare this value with the free stream Mach number, and use Figure 12.13 to solve for the coefficient of compressibility drag. Equation 16 shows the relationship necessary between the free stream Mach number and the crest critical Mach number at sweep.

(Equation 16)

Referencing Figure 12.13 in Fundamentals of Flight, it is clear that with a value of 1.12 for the comparison of the free stream and crest critical Mach number extrapolation will be necessary. The graph is clearly not linear, so linear extrapolation would yield an extremely inaccurate answer. Instead, a plot in Microsoft excel is generated to the best of my ability, with a third order polynomial to help estimate a result. Figure 14 shows the plot.

Figure 14 (Free stream/crest critical comparison)

Using the equation of the trend line and a value for x to be 1.12, a result of 0.0088 is achieved. The result can be viewed in Equation 17.

(Equation 17)

With the sweepback known, Cdc can be calculated using Equation 16. Using these values, and rearranging Equation 16, a coefficient of drag due to compressibility is calculated as 0.006547. Figure 15 is an excel program with the above calculations for drag due to compressibility.

Figure 15 (Drag due to compressibility)

Total Drag

With the coefficient of parasitic drag, drag due to compressibility, interference drag, and induced drag known, a summation of the three will result in the total drag coefficient. Adding the three values, a coefficient of drag, CD is approximately 0.0344. Knowing the coefficient of drag, the thermophysical properties, and the area of the wing, a total drag in lbs can be calculated. All values can be referenced in Figures 1 and 2. Equation 18 displays the equation to calculate the total drag on the aircraft.

(Equation 18)

In Equation 17, D is the drag in lbs, CD is the coefficient of drag, is the density in slugs/ft3, V is the velocity of the aircraft in ft/s, and S is the wing planform area in ft2. Substituting these values into Equation 18 yields a final drag.

The ratio of lift to drag can be seen in Equation 19, where the lift is the weight of the aircraft.

Figure 16 displays a Microsoft Excel program with the above calculations for the total drag. It also displays the percent each of the ratios for the three causations for drag.

Figure 16 (Total drag calculations)

Results

In this report, the total drag calculated on the 737-700 without winglets is 10,265 lbs. This seems fairly reasonable for a medium size transport aircraft traveling at a Mach of 0.785. Typical aircraft efficiencies of this size range between 0.75 and 0.9, according to Shevell in Fundamentals of Flight. For the calculations performed, an efficiency factor was calculated within this range at 0.803. The lift to drag also appears to be fairly low at 13.85. After speaking with a Boeing Engineer, Blake Singer, who was kind enough to share his knowledge, informed me that the 737 line had a typical lift to drag ratio between 17 and 19.

The error within these calculations can be seen from several different sources. There was a great deal of estimating, as well as extrapolating at times. A small error by itself may not attribute much to the total drag, but when the errors continue to add up, a significant amount of error can be accounted for. Some of the most difficult aspects of these calculations were finding the areas and chords for the nacelles and pylons. Using nothing but the AutoCAD drawings provided, it proved to be difficult in finding the wetted areas of nearly every component on the aircraft. Because the nacelles were not perfectly circular, and rather oblong, it made it extremely difficult to converge on final dimensions and wetted area. The pylons were also very difficult to attach dimensions and values to. The fuselage had an estimated wetted area as well. Because the parasitic drag comprises exactly half of the total drag, this source of error is clearly the largest and most significant in this project.

The induced and compressibility drag components attribute the majority of the remaining drag. As the induced drag relies on the parasitic drag coefficient, any estimation within the parasitic drag will lead to an error within the induced drag. The compressibility drag relied heavily on plots that did not provide a function to ensure an accurate answer. Extrapolation was used as well, which can attribute to an inaccurate result.

The plots and charts that were used in this report also pertained to studies done on separate aircraft. The data that Richard S. Shevell uses in Fundamentals of Flight often relates to one specific aircraft. This can be extremely misleading as it is applied to other aircraft.

Some of the initial values could also vary. For example, the weight used in these calculations was the average of the max take off weight and the max landing weight. The weight of the aircraft can vary greatly given the fuel and passenger loading. Even through the assumptions and estimations, a reasonable answer of the lift to drag as well as the total drag on the aircraft could be calculated.

While this project lists the steps necessary to find the drag on a Boeing 737-700 aircraft, it is clear that the results are reasonable, but not accurate. The plots, assumptions, and areas all attribute the error in finding the drag. The error in this project is about 18.5% to 27.1%. Given the assumptions and method to finding the areas, this is a reasonable estimation to the total drag on the aircraft.APPENDIX

Formulas

Equation 1: Average thickness/chord...

Equation 2: Reynolds Number...

Equation 3: Mean Aerodynamic Chord...

Equation 4: Coefficient of Drag: Wing...

Equation 5: Fineness Ratio...

Equation 6: Coefficient of Drag: Fuselage...

Equation 7: Coefficient of Drag: Horizontal Stabilizer...

Equation 8: Coefficient of Drag: Vertical Fin...

Equation 9: Linear Interpolation...

Equation 10: Coefficient of Drag: Nacelles...

Equation 11: Coefficient of Drag: Pylons...

Equation 12: Coefficient of Drag: Induced...

Equation 13: Coefficient of Lift...

Equation 14: Efficiency Factor...

Equation 15: Crest Critical Mach @ Sweep...

Equation 16: Ratio of Free Stream Mach to Crest Critical Mach...

Equation 17: Coefficient of Drag: Compressibility *UNIQUE TO THIS PROJECT ONLY... *

Equation 18: Total Drag...

Raw Data/Figures/Calculations

Plots

Figure 7: Fineness Ratio Plot

Figure 11: Lift-Dependent Drag Factor for Fuselage Interference

Figure 12: Efficiency Factor

Figure 14: Incremental Drag Coefficient Due to Compressibility

DrawingsReferences

1. "737 Family."Boeing: 737-700 Technical Characteristics. Boeing, 2014. Web. 9 Apr. 2014. .2. "Airport Reference Code and Approach Speeds for Boeing Airplanes." Boeing, 1 Mar. 2011. Web. 19 Apr. 2014. .3. "Boeing 737." Online interview. 14 Apr. 2014.4. Brady, Chris. "Detailed Technical Data."Boeing 737. N.p., 1999. Web. 9 Apr. 2014. .5. "Commercial Airplanes."Boeing: Airport Technology. Boeing, 2014. Web. 16 Apr. 2014. .6. Shevell, Richard Shepherd.Fundamentals of Flight. Englewood Cliffs, NJ: Prentice-Hall, 1983. Print.