Brandon Foster
MAE466
2/8/12
HW#2
1) I think about 1000 radial stations are required for a converged calculation. 2) The first plot is of a rotor with linear twist showing the lift coefficient variation with rbar in hover. The second plot is the lift coefficient max along the radius which looks to be about 1.2.

The maximum thrust of the rotor in hover in terms of thrust coefficient is 0.0183.
Cpo = 2.5668e-004
Cpi = 0.0020
Cpt = 0.0022
Cpideal = 0.0017
Fig Mer = 0.7832
MATLAB CODE:
First Code:
This function integrates using the composite trapezoidal method of a function f(x) that is given in a set of n discrete points.

function I = IntPointsTrap(x,y)
n = length(x)-1
a = x(1)
b = x(n+1)
h = (b-a)/n
s = 0
for i = 2:n
s = y(i)+s;
end
I = h/2*(y(1)+y(n+1))+h*s
Second Code: s=sigma t=theta l=lambda a=alpha
B = 4;
rbar = .001:0.001:1;
s = .1; a = (2.*pi)./(sqrt(1 - .4.*(rbar.^2))); t0 = 0.3; t1 = -.17;
t = t0 + t1.*rbar;
li = -(1/2).*((s.*a)./(8))+(sqrt((((s.*a)./(16)).^2)+((s.*a.*rbar.*t)./(8))));
f = (B./2).*((1-rbar)./li)
F = (2./pi).*acos(exp(-f));
l = -(1/2).*((s.*a)./(8.*F))+(sqrt((((s.*a)./(16.*F)).^2)+((s.*a.*rbar.*t)./(8.*F))));
phi = l./rbar;
ab = theta - phi;
Cl = a.*ab;
plot(rbar, Cl)
dCt = (s./2).*Cl.*(rbar.^2)
y = dCt(1:999);
x = rbar(1:999);
I = IntPointsTrap(x,y);
Ct =I
Cd = .0091 - .078.*ab + 1.02.*(ab.^2);
dCp0 = Cd.*(rbar.^3);
y = dCp0(1:999);
I = IntPointsTrap(x,y);
Cpo = I.*s./2
Cpi = 1.13.*(Ct^1.5)./(sqrt(2))
Cpt = Cp_o+Cp_i
Cpideal = (Ct^1.5)./(sqrt(2))
FigMer = Cp_ideal/(Cp_total)

...Coefficient of variation
Sample-> CY=s/x
1. A relative measure of dispersion
2. Adjusts for differences in magnitudes of the means.
3. Does not have units of measure
4. Allows for direct comparisons of mean-adjusted dispersion across different data sets.
Percentiles and quartiles
Coefficient of determination
The proportion of variation in the dependent variable ”explained” by the independent variable.
因變量的變化的比例“解釋”的獨立變量。
(Correlation coefficient)^2=r^2
R=0.90
(0.90)^2=0.81
Ex. Monthly income how much u spend on grocery, coefficient of determination
81%of your grocery billi being
19:% is not being explained(for reason we don’t know)
Maybe holiday month, having food, people….etc
Unexplained situation
CV fund 1 S/x=1.51
CV fund 2 S/x=1.30
Conclusion: Fund1 has greater relative dispersion than fund2
Correlation/ coefficient
*Data-data analysis-regression-INSERT input Xvariable/y variable
*Click blue square -Add trend line-display click
CH5.
Be familiar with the terms (different types of collect data)
1) Direct observation
2) Experiments
3) Survey
4) Telephone interviews
5) Self administered survey
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Slope rise/run, y/x
B1=2.25 2.25/1 = y/x
Every 1 unit 2.25 cents
B1=0.3 0.3/1=y/x
Slope intercept...

...The Airfoil & Theories of LiftAirfoil
Definition:
Have you noticed the curved shape of a bird's wing? An airplane's wing is curved also. A wing is designed for flight. It has a special shape called an airfoil. The airfoil shape provides a lifting force when air flows around it. Airfoil shapes can be found on wings, fans and propellers.
Importance:
An airplane’s airfoil plays a very important role in lifting the aircraft. The airfoil is designed to increase the velocity of the airflow above its surface, thereby decreasing pressure above the airfoil. Simultaneously, the impact of the air on the lower surface of the airfoil increases the pressure below. This combination of pressure decrease above and increase below produces lift.
Airfoil Behavior and Influence on an Aircraft:
As a wing moves through air, the air is split and passes above and below the wing. The wing’s upper surface is shaped so the air rushing over the top speeds up and stretches out. This decreases the air pressure above the wing. The air flowing below the wing moves in a straighter line, so its speed and air pressure remains the same. Since high air pressure always moves toward low air pressure, the air below the wing pushes upward toward the air above the wing. The wing is in the middle, and the whole wing is...

...Section 4 Thurs. 2:10 PM
Report Type:
Internal Report
Title of Experiment:
Aerodynamic Lab: Lift and Drag on an Airfoil
Date Experiment Performed:
03/29/2012
Date Report Submitted:
04/12/2012
Names of Group Members:
Grader's Comments:
Michael Stevens
Grade:
Abstract:
The Aerodynamics Lab: Lift and Drag on an Airfoil experiment examined the lift
and drag on a NACA 0012 airfoil inside a wind tunnel. The objective of the experiment
was to obtain information relating to the lift and drag of the airfoil, such as lift forces, liftcoefficients, drag forces including its contributors, and drag coefficients. The data was
analyzed using Matlab by two different methods, through pressure distributions, and
through a force balance. Approximations of the lift and drag data to compare with the
experiment results were attempted to test which methods were effective, or not effective.
These approximations were conducted using a Javafoil simulation, and also using thin
airfoil theory.
The lift forces calculated from the pressure distribution measurements were
slightly higher than the directly measured forces from the force balance, however, the
pressure distribution measurements followed the same trend as the force balance data.
This...

...Homework 1 Due Monday, September 17th at the beginning of class. Show your work. 1. Match the diﬀerential equation in (a)-(c) to a family of solutions in (d)-(f). The point of this exercise is not to solve the diﬀerential equations in a) - c). (a) y = y 2 (b) y = 1 + y 2 (c) yy = 3x (d) y = tan(x + C) (e) 3x2 − y 2 = C (f) y = −1/(x + C)
2. Find the value of k so that y = e3t + ke2t is a solution of y − 2y − 3y = 3e2t . 3. Solve the following diﬀerential equations and IVP’s. You may solve these equations implicitly. (a) y + 3x2 y = x2 (b) y ln t = y+1 t
2
dy dt
2 sin t dy = 0 y (d) y y − t = 0, y(1) = 2, y (1) = 1 (c) cos t dt + 1 + (e) y − y = et y 2 (f) cos(xy) − xy sin(xy) + 2xyex + (ex − 2y − x2 sin(xy))y = 0, y(1) = 0 dy x + 3y (g) = dx 3x + y 2 x sin x dy + (y cos3 x − 1) dx = 0, 0 < x < π (h) cos (i) (x + yey/x )dx − xey/x dy = 0, y(1) = 0 [Hint: Think homogeneous.] 4. Suppose the diﬀerential equation dP = (k cos t)P, dt is a model of the human population P (t) of a certain community, where k is a positive constant. Discuss a (non-morbid) interpretation for the solution of this equation. In other words, what kind of population do you think it describes? [Actually solving the equation is not helpful.] 5. Write down a diﬀerential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. (Remarks: Consider the forces acting on a falling object, and what they must add up to by...

...Variations in Humans
Aim: To find the differences in human size from measurement
Apparatus: Seven to five friends, measuring tape
Method:
1. Choose five/seven friends
2. Take height of each person
3. Record data in appropriate manner
4. Process data collected
5. Make evaluation
Observation: The males in most case were taller than the females and had a general height of 5 feet 8 inches, while the females remained in the area of 5 feet and 1 inch to 5 feet and 2 inches.
Theory: Every human is not the same there are slight to major variations in size with every human being. Human variability, or human variation, according to the Wikipedia online encyclopedia is the range of possible values for any measurable characteristic, physical or mental, of human beings. Differences can be trivial or important, transient or permanent, voluntary or involuntary, congenital or acquired, genetic or environmental.
Analysis of data: The general height for males was about 5 feet 8 inches with only two exceptions being half and third of an inch taller. The females however were much shorter the tallest being 5 feet 2 inches. Height with the males may have shifted a little based on head shape and body structure, whereas the females having much more hair could’ve added the extra inches of difference.
Source of error: Shoes and hair could cause inaccurate measurements, poor posture and cranium structure. Tape measure may not have...

...LIFT, DRAG AND MOMENT OF A NACA 0015 AIRFOIL
by Steven D. Miller
DEPARTMENT OF AEROSPACE ENGINEERING
THE OHIO STATE UNIVERSITY
28 MAYi 2008
ABSTRACT
A NACA 0015 symmetrical airfoil with a 15% thickness to chord ratio was
analyzed to determine the lift, drag and moment coefficients. A 2D airfoil was placed
in a low speed wind tunnel with pressure taps along its surface and a pitot probe
downstream to measure the flow characteristics. The wind tunnel was operated at a
nominal 17 m/s during the coefficient measurements, a Reynold's number of about
232,940. The airfoil, with an 8 in chord, was analyzed at 0, 5, 10 and 15 degree
angles of attack. The phenomenon known as hysteresis with regards to stall
conditions was also observed by varying the angle of attack and wind tunnel
velocity.
ii
TABLE OF CONTENTS
Page
List of Figures iv
List of Tables iv
Nomenclature v
Chapter
I. Introduction 1
II. Apparatus and Instrumentation 2
III.Experimental Procedure 4
IV. Analysis 5
V. Results and Discussion 7
VI. Conclusions 13
Appendix 14
References 18
iii
LIST OF FIGURES
LIST OF TABLES
iv
Figure Page
1 NACA 0015 Airfoil Cross-section with Pressure Taps 2
2 Pressure Distribution at 0 Deg Angle of Attack 8
3 Pressure Distribution at 5 Deg Angle of Attack 9
4 Pressure Distribution at 10 Deg Angle of Attack 9
5 Pressure...

...Though he promised to work with Congress, the President also made clear that he would search for ways to go around them "whenever and wherever I can" if they do not cooperate. The President mentioned the College Opportunity Summit, which DSpar attended, to work on making college education a reality for all students. The President then received a thumbs up from Speaker Boehner after a reference to his humble beginnings as a barkeep's son. Boehner sat stone-faced the rest of the night.
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"Listen, China and Europe aren’t standing on the sidelines; and neither, neither should we. We know that the nation that goes all-in on innovation today will own the global economy tomorrow. This is an edge America cannot surrender."While Obama proudly declared that his "all of the above" energy plan is working to make energy independence a reality, he focused primarily on natural gas. While a step-up from foreign oil, natural gas is not always "extracted safely," i.e.fracking. He mentioned solar power and asserted that tax reform must prevent Big Oil from receiving $4 billion a year, so that this money can be invested in alternative fuel sources. And, to...

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Lift The Ban
Pit bulls are the most lovable and loyal type of dogs until they are placed into the hands of the wrong trainers who mistreat, neglect and use them for fighting. Pit bulls used to be one of the most well-liked pets and they used to represent the American Military. Over the years the pit bull became used for fighting dogs and that’s how they received such a bad rep. They are illustrated by many as these fierce, aggressive dogs who are trained to kill. But are they really as bad as people portray them to be. Because of the portrayal many place on pit bulls they have become banned in numerous places including just about every military installation. The Breed Specific Legislation (BSL) what the ban on pit bulls is currently known as, bans or limits specific breeds based on the fact they are known to be dangerous. Not every pit bull is dangerous. It’s time for owner’s to take responsibility for these vicious attacks, not the pit bulls and its time to lift the ban.
Why should the pit bull be banned? Pit bulls are not humans so why would you ban the one who doesn‘t understand and is only doing what they are taught. No matter what the myths or what the media portrays about pit bulls they are not at all what some describe. Yes, there are pit bulls that kill and are trained to kill but that’s not the case for all pit bulls. I am one who can testify to that. I owned a pit bull for a couple of years, he was a lovable...