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Sec ARO101A 3 Introduction to Aerospace Engineering
Plane Experiment AKA Operation Crash and Burn
Wesley McGinn Jennifer Kurashige Jerome Magsino Thunyapoj Kijroongruangsri (JOE)
November 22, 2006
Executive summary The purpose of this project is to use a model plane and fly it over a know course length in order to make calculations for: the lift coefficient CL, the drag coefficient CD, the power required for flight, and the lift-to-drag ratio L/D. This model plane was used to simulate actual aircraft flight so that we could get a hands on feel for what a plane does during flight. To calculate the CL we used the airspeeds (V ) on 15 lengths of the course in order to calculate the individual CL's and CD's for each course. Another task required was to graph the V2 vs the CL. This project also was intended for us to use and develop some problem solving and team skills; as well as, help use to gain some general knowledge of the aerospace engineering field. From our data we found that on average our plane took about 6 seconds to fly the course of 140ft (42.672 m). We had an average CL of .694 which seems correct since the max is around ~1.0-1.5. When we initially tried flying the plane there was a fair amount of wind but, the later it got the less wind there was till there was practically none. We used that time frame so that we would not have to account for the wind speed. Throughout this project we kept in our minds how much error we each could be bringing into the equation while calculating various things. We knew that every time we crashed the plane might have more drag since it will have damaged or crumpled parts. Also our way of measuring the times is fairly inaccurate because it's based on 2 peoples reaction times really, so that could account for the biggest problem. Another factor is whether it was a straight line each time. This will increase the time and thus throwing off our velocity each time and impacting pretty much all the calculations. We could minimize these type errors if we had a GPS or something of that sort on the plane or just launched each time further from our initial start distance and then just clocked the straight away and repeated it each time, granted this would take longer to setup but in the end it would eliminate more of the inaccuracy of the time measured.
Discussion Modify this section and reword it NOT OURS the table is our data though In order to fulfill the objective of calculating the coefficient of lift for six trials, first we needed to understand the theory behind the coefficient of lift. The lift coefficient (CL) is a number associated with a particular shape of an airfoil, and is incorporated in the lift equation to predict the lift force generated by a wing using this particular cross section. The equation for lift coefficient is equal to: In this equation, L is the lift force, is the air density, V is the airspeed and A is area of the wing. The equation for dynamic pressure = q = v2. So the coeffient of lift equals the lift force divided by both the dynamic pressure and wing area, which is also called SW . One aspect of the coefficient of drag to notice is that it is a dimensionless number. Like the drag coefficient of say a car or an aircraft, the lift coefficient is a number that describes a characteristic amount of aerodynamic drag caused by fluid flow.While working through the experimental process, we had to examine and measure most of the characteristics of the airplane itself, such as the wing, vertical wing, and horizontal wing. The model that we worked on was an aircraft composed of various parts that required careful assembly. It consisted of a motor, which was powered by a
rechargeable battery pack. All the materials necessary were included in our package such as the main wing, horizontal wing (stabilizer), vertical wing, fuselage, propeller, wheels, and the remote control. Before building and flying our plane, we took basic measurements for later calculations. For example, in measuring the area of the horizontal wing, and vertical wing, we traced the actual parts onto engineering paper and counted the squares inside the wing outlines. We calculated that four little squares is equal to one square cm. So we simply counted the squares and then converted cm2 to m2 so that it conformed to the standard of the SI system of units. We calculated a horizontal tail area of 0.032 2 2 m and a vertical tail area of 0.014 m . For the main wing, we separated it into two long rectangles and two wing ends. We measured the rectangles with a ruler and traced the wing ends on graph paper and counted the squares. Finally, adding the two together we got the area of the entire main wing, which was 0.172 m2. Other calculations involving the mass were done with a scientific scale. Hence, the mass of our plane was 264 g and the mass of the battery pack was 105.6 g. These and other measurements can be seen in the following table.
V 1 2 d t V2 P 1 2 V2 P 1 1 2 V12
CL L q Sw
q
Drag
power efficiency V
Parameter area, m2 Area ratios Weight Wing Loading W/S Wing span, b Croot root chord t (thickness) t/c, % h (camber) h/c, % CG location CG % Croot
Wing Sw 0.242
Horizontal Tail SH 0.051 Area ratio SH/SW 21%
Vertical Tail Sv 0.009 Area ratio SV/SW 3.7%
4.76 N 15.04 N/m2 1.045 m 0.232 m 0.03 m 12.9% 0.015 m 6.5% 0.09 m (aft of LE) 38.8%
Modify this section and reword it NOT OURS The testing procedures for the aircraft consisted of measuring the time it would take our plane to travel from one end to the other of a set course length. In our experiment, our course length was about 60.96 m (or 200 ft.). In order to acquire these times, we had two people with stopwatches stand on one side of the 61 m course and another person stand on the other side of the course; this, of course, all happened while another person flew the plane. When the aircraft
passed the person on the other end of the course, he signaled the rest of the group by raising his arm in the air. When the two people with stopwatches saw this signal, one started the stopwatch while the other stopped his stopwatch. This person who stopped the stopwatch reported his time to the last group member, who wrote down the different times for the 12 passes. Therefore, by flying the aircraft and back forth as straight as possible and using a stopwatch to measure how long it took the plane to travel each of the 12 passes, we found the average upwind velocity and the average downwind velocity. To find the average upwind and downwind times, we separated our upwind ( V - Vw ) and downwind ( V + Vw ) times, added the different times it took to fly back and forth and then, and then divided by the number of attempts done in each direction. Our resulting average upwind velocity was 6.701 m/s and our average downwind velocity was 7.546 m/s. The setting, or geographical position where any plane is flown is always vital. In this experiment, our plane was flown over the engineering meadow on the Cal Poly Pomona campus. How would the geographical location of Cal Poly affect the aerodynamics of the plane? What this question is basically asking is how changes in altitude and air density could affect the flight of the model plane. First, we needed to find the altitude over the engineering meadow. We found this altitude by pinpointing the Cal Poly engineering meadow on Google Earth . This is a program that displays a topographical map of large cities on the earth. The altitude we found was approximately 228.6 m. We then calculated the air density by using the website aero.stanford.edu/StdAtm.html. This site automatically made standard atmosphere computations when we inputted altitude, speed, and reference length. We found the density () to be 1.198 kg/m3 . Since Cal Poly's altitude was, relatively speaking, slightly higher than sea level, the air density was slightly lower. The less dense the air, the less efficient the plane becomes at displacing air. Therefore, it was important to usethe numbers for Cal Poly's altitude and air density, or else we would have overestimated the coefficient of lift. Now that we got the altitude and density over Cal Poly, we used all our data to find the coefficients of lift. As stated earlier, the formula for lift coefficient is equal to: We then inputted the dynamic pressure, area of the main wing, and the lift force, which must be equal and opposite to the weight ( F=mg ), of the plane. The highest CL was 8.932 and occurred during the 6th trial. The average CL was 2.944. And finally, the smallest CL was 0.068 and occurred during the 2nd trial. The following is a chart that compares the coefficient of lift and (airspeed)2 .
INSERT V^2 vs Cl chart here
Modify this section and reword it NOT OURS In calculating this graph, we assumed the altitude and air density to be constant throughout the flight. In finalizing our data and calculations, we noticed that in the equation for the coefficient of lift, the lift force and the area of the wing are constant. Thus, only dynamic pressure changes the actual value of C L. And since density is assumed constant, the only variance in the coefficient of lift occurs in the change of airspeed. For example, as airspeed increases, the CL decreases. Because the airspeed is squared in the equation for the coefficient of lift, the graph should be curved.
Conclusion The Hands-On Aircraft Flight Testing Class Project was a difficult assignment because there were so many possibilities for error. First we had to acquire all of the supplies and materials needed to build the airplane. The procedure of building the airplane wasn't too difficult besides the fact that it took a long time to build the plane since there were so many little details in building the actual plane like using the right kind of glue on certain parts and the tedious job of sanding and taping most of the foam parts of the plane including the wings, rudder and elevator. Flying the plain was one of the most difficult parts of the project because none of us had any experience flying model airplanes. Our lack of experience resulted in four crashes. The crashes were mainly because we were not used to the controls of the plane and didn't know how to properly fly the plane. In total, there were seven crashes, four by the students in our group and three by Professor Edberg. One reason most of the groups, including our group, had problems is because we didn't create enough dihedral with the wings which prevented the plane from turning properly. Since the plane doesn't have ailerons, the dihedral wings were used so it was possible to control the plane with only the elevator and rudder controls. Without enough dihedral the plane was able to turn but to get the plane out of the turn and level it out was very hard. If we were to build another plane we would add a lot more dihedral or add ailerons so we can control the plane better. Another possible source in our calculations could be from not flying the plane straight every time and our lack of experience with controlling the plane. When Dr. Edberg flew our plane, the combination of wind and lack of dihedral, created a nonuniform flight every time we recorded the time for the plane to travel the distance we set up. Wind could of made the plane faster or slower and created a change in speed and when traveling up or down wind. When releasing the plane for takeoff, sometimes the pilot and the person who released the planes were different people so it was hard to tell when to release the plane. The person who released the plane sometimes threw the plane, which made the plane to loop upwards and then come straight down and crash. Two, almost three, of our crashes were because of this reason combined with inability to properly fly the plane. We could have avoided this if we built our plane better and if we all had more time to get accustomed to the controls of our own plane.
References
Anderson, Jr. John D. Introduction to Flight, Fifth Edition. McGraw-Hill Series in Aeronautical and Aerospace Engineering 2005 Edberg, Don. "Fluid Flow Exercises". 05 HW5-pitit-static+flow.doc, 2005 Edberg, Don. "NACA Airfoils Worksheet". 05 HW6-Lift-Airfoil Wksht.doc, 2005 "Lift Coefficient." Wikipedia: The Free Encyclopedia. 12 Nov. 2005, 1:00 PTC. Accessed 22 Nov. 2005 <http://en.wikipedia.org/wiki/Lift_coefficient. "Topozone California State Polytechnic Colege, USGS San Dimas (CA) Topo Map." Topozone.com. 2006. 15 Nov, 2006. <www.topozone.com/map.asp?lat=34.0579&lon=-117.8225>

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Technion - MATH - Infi 2

2A4'qn milibxz oeilb -104281- 2 itpi`.mixdva12 : 00dry cr -27.12.2006:dybd jix`zlcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfzz`e cinlzd my z` xexiaa oiivl `p .micigia dybdd .wcedn yibdl `p .mixq

Technion - MATH - Infi 2

5 oeilib -2007 aia` - (104281) 2 itpi`13 : 00 ,4.7.2007,iying mei :dybd jix`zxiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz xexiaa oiivl `p .micigia dybdd .wcedn yibdl `p .mixqlw e` zeiwy `llA4lcebn.xry sca jxev

Technion - MATH - Infi 2

2 oeilib -2007 aia` - (104281) 2 itpi`13 : 00 ,12.4.2007,iying mei :dybd jix`zxiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz xexiaa oiivl `p .micigia dybdd .wcedn yibdl `p .mixqlw e` zeiwy `llA4lcebn.xry sca jxev

Technion - MATH - Infi 2

3A4'qn milibxz oeilb -104281- 2 itpi`:dybd jix`z.(ef dryl jenq sq`p libxzd !xg`l `l `p) mixdva12 : 00dry cr -17/1/2007lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfzz` xexiaa oiivl `p.micigia dyb

Technion - MATH - Infi 2

5A4'qn milibxz oeilb -1042815/6/2006- 2 itpi`:dybd jix`z.(ef dryl jenq sq`p libxzd !xg`l `l `p) mixdva12 : 00dry cr -lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfzz` xexiaa oiivl `p.micigia dybdd

Technion - MATH - Infi 2

:3 libxzl fnx:miiwzn ik al eniy|gn (x) - f (x)| = n = n n1 x+ n f (t)dt - f (x) x 1 x+ 1 x+ n f (t)dt - n x n x 1 x+ n |f (t) - f (x)| dt xf (x)dt:2 sirq 4 libxzl fnxze`xdl lw- a leabde zetivx i"r .|f (x)|<M- y jkMmiiw okl dneqg