matlab code

NUMBER 1; Write a small matlab program to compute the maximum height when the rocket is fired straight up. Assume no wind. In order to get reasonable consistency of answers, use dt = 0.1 second . thrust= [0.0,6.0,14.0,5.3,4.9,4.2,4.2,4.5,4.5,4.6,4.5,4.5,4.5,4.5,4.6,4.6,4.5,4.5,0.0,0.0]; time= [0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.0]; Estes Alpha III Length 12.25 inches = 0.311 meters Diameter 0.95 inches = 0.0241 meters Body area 0.785 square inches = 0.506E-3 square meters cross section Cd of body 0.45 dimensionless Fins area 7.69 square inches = 0.00496 square meters total for 3 fins Cd of fins 0.01 dimensionless Weight/mass 1.2 ounce = 0.0340 kilogram without engine Engine 0.85 ounce = 0.0242 kilogram initial engine mass Engine 0.33 ounce = 0.0094 kilogram final engine mass Thrust curve Total impulse 8.82 newton seconds (area under curve) Peak thrust 14.09 newton Average thrust 4.74 newton Burn time 1.86 second Initial conditions: t = 0 time s = 0 height v = 0 velocity a = 0 acceleration F = 0 total force not including gravity m = 0.0340 + 0.0242 mass Basic physics: Fd = Cd*Rho*A*v^2 /2 two equations, body and fins Fd is force of drag in newtons in opposite direction of velocity Cd is coefficient of drag, dimensionless (depends on shape) Rho is density of air, use 1.293 kilograms per meter cubed A is total surface area in square meters v is velocity in meters per second (v^2 is velocity squared) Fg = m*g Fg is force of gravity toward center of Earth m is mass in kilograms g is acceleration due to gravity, 9.80665 meters per second squared Ft = value from thrust curve at this time, you enter this data. Do not copy! This is part of modeling and simulation. start with first non zero thrust. F = Ft - (Fd body + Fd fins + Fg) resolve forces a = F/m a is acceleration we will compute from knowing F, total force in newtons and m is mass in kilograms of body plus engine mass that changes dv = a*dt dv is velocity change in meters per second in time dt a is acceleration in meters per second squared dt is delta time in seconds v = v+dv v is new velocity after the dt time step (v is positive upward, stop when v goes negative) v+ is previous velocity prior to the dt time step dv is velocity change in meters per second in time dt ds = v*dt ds is distance in meters moved in time dt v is velocity in meters per second dt is delta time in seconds s = s+ds s is new position after the dt time step s+ is previous position prior to the dt time step ds is distance in meters moved in time dt m = m -0.0001644*Ft apply each time step t = t + dt time advances print t, s, v, a, m if v < 0 quit, else loop Ft is zero at and beyond 1.9 seconds, rocket speed decreases Published data estimates a height of 1100 feet, 335 meters to 1150 feet, 350 meters. Your height will vary. Your homework is to write a program that prints every 0.1 seconds: the time in seconds height in meters velocity in meters per second acceleration in meters per second squared force in newtons mass in kilograms (just numbers, all on one line) and stop when the maximum height is reached. NUMBER 2: In a MATLAB, write a program that does a least square fit of the thrust data used in NUMBER 1. Use your data x = 0.0 0.1 0.2 ... 1.9 y = 0.0 6.0 14.1 ... 0.0 Be sure time 0.0 has value 0.0, time 1.9 has value 0.0 Do the least square fit with 3, 4, ... , 17 degree polynomials. Compute the maximum error, the average error and RMS error for each fit. If convenient, look at the plots of your fit and compare to the input. Print out your data. Remove excess printout, print: Print out your polynomial order for each degree 3..17 and print out maximum, average and RMS error for each.