HOMEWORK ASSIGNMENT #8

ME 303 FLUID DYNAMICS/ WESTPHAL/ WSU/ FALL 2000

• Follow the Homework Guidelines for preparing your submission.
• You are encouraged to work together with other students, but the work you submit cannot be a machine-produced duplication of another student's work - it must be an original, but can represent your version of a collaborative effort.
• Late work not accepted!

The assignment consists of the problems given below.

1. 11.66 OMIT DISCUSSION.
   
   
2. A "powered parachute" sold by Six-Chuter Inc. of Yakima is a relatively new type of ultralight aircraft that uses a modern parasail (sort of a flow-through parachute) with 36 ft span by 12 ft chord which functions as the wing. This pusher-type, propellor-driven aircraft, with a total weight ("wet", including fuels and lubricants, as well as the pilot) of 540 lbf, achieves 26 mph in level cruising flight powered by a 40 hp Rotax engine. Answer the questions below; no other DISCUSSION required.
   • What are the wing planform area and aspect ratio?
   • Determine the lift coefficient for level cruising flight.
   • Estimate the drag coefficient for the entire aircraft during level cruise. NOTE: for this part you may assume... (1) propulsive power is 75% of shaft power, and (2) the engine setting is 80% of rated power at level cruise.
   
   
3. Select ONE single or twin-engine, general aviation aircraft (e.g., Cessna 172, Piper Cub, Beech Bonanza, etc.) and find its ...
   • maximum gross take-off weight;
   • wing chord, span, and area
   • nominal take-off speed
   • nominal cruise speed
   • stall speed
   • engine rated thrust or horsepower and if available, cruise power requirement
   Based on the above information, calculate
   • wing aspect ratio
   • nominal cruise drag and lift coefficients, cruise L/D
   • take-off lift coefficient
   • maximum (stall) lift coefficient
   • thrust/weight ratio
   OMIT DISCUSSION. Here are some suggested sources of information...
   • Jane’s Aviation Encyclopedia,
   • the WEB,
   • Jane’s All the World’s Aircraft,
   • AOPA Pilot Magazine,
   • Flying Magazine,
   • Pilot's Operating Handbook ("POH") for an actual airplane (BEST source!)
   
   
4. Show that, for constant-velocity unpowered (gliding) flight, the glide angle (in radians) approximately equals the drag to lift ratio, C_D/C_L. DISCUSSION: Why might one care about the C_D/C_L value for a powered light aircraft?
   
   
5. Using your result from problem 2 of homework #7 for the Cessna 152's friction drag is approximately equal to its zero-lift (parasitic) wing drag, C_D0, what would be the wing drag coefficient C_D and the power required to overcome wing drag in cruising flight assuming ideal (elliptical) wing loading? The aircraft weight can be taken as 7 kN; use wing dimensions and cruise speed/properties from the earlier problem statement. DISCUSSION: Calculate the lift to drag ratio C_L/C_D... could a different C_L (which would require more wing area) result in a higher lift to drag ratio?
   
   
6. 11.69 NOTE: there is a typo in the equation for C_D... it should read: C_D = C_D0 + C_L²/(PI * ASPECT RATIO); also, the term should be "winG loading" rather than "winD loading". HINT: try just plotting power vs. velocity! DISCUSSION: In light of the fact that power is proportional to speed CUBED, how can you explain this result?
   
   
7. 11.75 Hint: to find the min/max of a function, set its derivative to zero. OMIT DISCUSSION