MAE 3241 Hmk 1

8/6/2019 MAE 3241 Hmk 1

http://slidepdf.com/reader/full/mae-3241-hmk-1 1/2

MAE 3241: Aerodynamics and Flight Mechanics Assigned: January 19, 2011

Homework #1 Due: January 31, 2011

Answer the following questions:

1. Estimate the Reynolds number at cruise conditions over the wing of the world’s largestcommercial airplane, the Airbus A380 (http://www.airbus.com/en/). Is the boundary layer 

laminar or turbulent?

2. Estimate the Reynolds number at the tip of the rotor blades on the Sikorsky Blackhawk helicopter (www.sikorsky.com) at sea-level conditions. Use a Reynolds number based on

the chord of the rotor blade.

3. Explain how a helicopter flies forward.

Complete the following problems from Fundamentals of Aerodynamics:

1.2, 1.3, 1.4, 1.5, 1.6, 1.9, 1.13

Answer the following question about wind tunnel testing of the Boeing 787:

Boeing is interested in developing an enhanced cargo capacity version of their new 787

commercial airplane (http://www.boeing.com/commercial/787family/index.html). The new

version will fly at a Mach number of 0.8 at an altitude of 10 km. The vehicle has a wing chord of 

10 meters. A few pictures of the 787 are shown below for reference:

Figure 1: Boeing 787 Figure 2: Boeing 787 Wind Tunnel Testing

Your job as a new engineer is to help Boeing’s engineering management team make sound

choices regarding wind tunnel testing facilities for this new airplane. To help make thesedecisions, answer the following questions:

1) What is the chord Reynolds number for this vehicle at the stated cruise conditions?

2) This plane must be able to operate at all world airports, year round. For argument’s sake,assume that it must be able to take-off (and land) in conditions ranging from seal level

(Orlando) to 1.5 km altitude (Mexico City), and in temperatures ranging from -40 ºF

1

8/6/2019 MAE 3241 Hmk 1

http://slidepdf.com/reader/full/mae-3241-hmk-1 2/2

(Anchorage) to 120 ºF (Cairo). Taking into account the variation of density and viscosity

with both temperature and pressure, what is the range of chord Reynolds numbers that the

aircraft experiences during take-off? The proposed take-off speed is 160 MPH.

3) During the development of this aircraft, Boeing engineers want to do scale model testing

of the vehicle at cruise conditions (Mach = 0.8, altitude = 10 km). Clearly, full-scaletesting is not possible. For each of the following test facilities, compute one or two

  possible testing scenarios (model size, wind speed, temperature and pressure) for 

achieving perfect Mach number and Reynolds number similarity. For each condition,discuss the pros and cons of the required testing facility, the difficulties that one might

encounter and other factors that you think are important (economic, environmental,

structural, etc.).

a. High Pressure Wind Tunnel (air at 4 atmospheres, room temperature) b. Cryogenic Wind Tunnel (Nitrogen at 100 K, atmospheric pressure)

c. Heavy Gas Wind Tunnel (Xenon gas at atmospheric temperature and pressure)

Given these facilities, what might be an ideal testing combination you would recommendto Boeing management?

 Notes on density and viscosity of simple (ideal) gases:

Density: The density depends strongly on both the temperature and pressure and may be

computed from the ideal gas law.

Viscosity: The viscosity of a gas is strongly dependent on the temperature and less so on

 pressure. For these questions make use of the following form of Sutherland’s law for viscosity,

which may be expressed as:

 BT 

 AT 

+

=

5.1

 µ 1

A and B are constants which depend on the test gas and T is the temperature in Kelvin. The

viscosity, µ , is in units of N s/m2 or kg/m s. The table below contains the constants, A and B, for 

the various gases employed in the wind tunnel facilities:

Table 1: Selected Test Gas Properties

Test Gas A BAir 1.46x10-6 110

 Nitrogen 1.36x10-6 104

Xenon 2.45x10-6 252

2