Download data, calculations, reason, and apply sheets

DATA, CALCULATIONS, REASON, AND APPLY SHEETS
Finding the distance from the liftoff point to where the angle is measured is found with a
50 or 100 foot tape measure. This is the ground distance d.
This distance is the adjacent leg in the Trigonometric ratio, Tangent of A: Tan Angle =
Opposite / Adjacent. The “Opposite” then is the Altitude that we are finding for the
rocket at various stages of flight. The equation then can be written:
Altitude = Ground Distance (with tape) x Tan Angle ( Angle from observer level to
flight-event).
Altitude = d x Tan A
Angle from liftoff point to white smoke = A(1) = ___________degrees
Angle from liftoff point to maximum altitude = A(2) = ___________degrees
Angle from liftoff point to appearance of parachute = A(3) = __________degrees
To find the needed Vertical Distances for equation 2 and equation 3 using the measured
altitudes:
Altitude(1) = d x Tan A(1) + 5.5
Altitude(1) = __________
(d: Ground distance using tape, A(1): See above,
(+ 5.5: Compensate for height of observer.)
Altitude(2) = d x Tan A(2) + 5.5
Altitude(2) = ____________
(d: Ground distance using tape, A(2): See above,
(+ 5.5: Compensate for height of observer.)
Altitude(3) = d x tan A(3) + 5.5
Altitude(3) = ____________
(d: Ground distance using tape, A(3): See above,
(+ 5.5: Compensate for height of observer.)
D(1): Distance from ground to white smoke of rocket motor
D(1) = Altitude(1) = _____________
D(2) = Distance to maximum height of rocket due to the force of gravity stopping
rocket’s vertical upward motion.
D(2) = Altitude (2) = ___________
D(3) = Distance from maximum altitude, Altitude(2) to Altitude of rocket when the
parachute is forced out of rocket Altitude(3).
D(3) = Altitude(2) =
_________
1) The value of V is needed by evaluating equation 1 using the data for the rocket you
will fly. V is the maximum velocity achieved by the rocket at the altitude when the rocket
motor thrust stops (No more fuel). V will be needed in equation 2 to determine the time t
of the rocket when the rocket motor stops to when the rocket reaches maximum altitude.
Equation 1:
V = [ ( Total Impulse / (Burn Time t x Weight of the Rocket ) - 1 ] x 32t
Total Impulse (Ounce-sec) and Burn Time (Sec.): See ATTACHMENT STUDENT
DATA WORK SHEET ( From Manufacture). Note: To convert Total Impulse from
Newton-sec to Ounce-sec multiply Newton-Sec value by 3.60. Also, the time in the last
term 32t is also the Thrust Burn Time from the manufacturer. The weight of the rocket is
the average lift weight which is the sum of the weight of the rocket with fuel (See data
sheet) and without fuel (see data) divided by two.
Remember to convert Newton-Sec to Ounce-Sec. Rather than pounds of thrust we have
ounces of thrust. (If you wish you could convert units from Pounds-Feet-Seconds to
Newtons-Meters-Seconds)
V = _____________
2) Theoretical time of flight from liftoff to opening of parachute calculated from
equations one, two, and three.
T(total) = t(eq-1) + t(eq-2) + t(eq-3) = _____ + _______ + _______ = _________
t(eq-1) = Total burn time of the rocket motor. Find this time in rocket motor
specifications supplied by ESTES or other manufacturer.
T(eq-1) = ________
t(eq-2) = Time of flight from the moment the thrust stops (white smoke) to the moment
when the rocket reaches maximum altitude when the rocket stops its vertical motion due
to the negative force of gravity. To obtain t(eq-2) you must evaluate equation 2 and then
solve for the unknown t which is the time of flight for this segment.
Evaluating Equation 2:
Y = -1/2gt² + Vt + S˳
Rewriting equation 2:
D(2) = -1/2gt² + Vt + D(1)
(g = 32 ft/sec², V = Maximum velocity-see
V above, S ˳ = Altitude at the point when the
thrust ends D(1), Y = Maximum altitude of
rocket D(2). )
Equation 2 is a quadratic equation with time t as the independent variable. Solve for t
using the quadratic formula. Remember this value for t(eq-2) is the time of flight for the
rocket from the end of thrust to the maximum altitude of the rocket. Remember only the
positive value is t(eq-2).
t(eq-2) = _______
t(eq-3) = Time of flight from the maximum altitude D(2) to the descent of the rocket to
the event when the parachute opens.
Y = -1/2gt² + V ̥ t + S ̥̥
( g is 32ft/sec², t is the time from maximum
Altitude to event of opening of parachute, V ̥
is velocity when the rocket reverses its upward
course, therefore V ̥ = 0, S ̥ is the altitude at
maximum altitude, D(2). Y is the altitude at
the event of the parachute opening, D(3).
Rewriting equation 2:
D(3) = -1/2gt² + D(2)
Solve equation 2 above for t and the resulting positive value for t is t(eq-3).
t(eq-3) = _______
Therefore :
T(total) = t(eq-1) + t(eq-2) + t(eq-3) = __________
Analyses:
1) Compare theoretical to experimental : Above (total) / Stopwatch time in Data Work
Sheet
(Theoretical / Experimental) x 100 = _______ / ________ = _________
2) G Forces experienced by the rocket or the number of gravities the rocket
experienced.
Start with the Equation 1:
V = [Total Impulse / ( Burn Time x Weight of Rocket) – 1 ] x 32t:
Evaluate: [ Total Impulse / (Burn Time x Weight of Rocket) - 1 ]
Impulse = Force from thrust x t. Force from thrust = mass x Acceleration (From
thrust)
Therefore: Impulse = Force x t = mass x acceleration x t
(Burn Time x Weight of Rocket ) = ( t x force on the rocket from gravity or one G)
Back to equation one:
[ Total Impulse / ( Burn Time x weight of Rocket) -1] =
[ mass x Acceleration from thrust x t / ( t x mass x acceleration from gravity) -1]
This simplifies to : [ ( Force of thrust / force of gravity ) -1 ]
Subtract one from the force when the rocket is sitting on the ground.
The number of G’s the rocket experiences =
Thrust -from rocket data / (weight of rocket-average ) -1 = _______ / _________
G’s = __________