Linear Motion
- Acceleration and Force -
F = m a
F = Force in Newtons
m = mass in Kg
a = acceleration (m/s)
- Weight
-
F = m g
F = Force in Newtons
m = mass in kg
g = acceleration due to gravity (constants)
- Average Velocity -
Vavg = d / t
Vavg = Average Velocity (m/s)
d = Distance (m)
t = time (s)
- Average Acceleration
-
a = v1-v0 / t1 - t0
a = Acceleration (m/s/s)
v1 = veloctiy 1 (m/s)
v0 = velocity initial (m/s)
t1 = time 1 (s)
t0 = initial time (s)
- Constant Accereation -
v = v0 + at
v = Velocity (m/s)
v0 = velocity initial (m/s)
a = acceleration (m/s/s)
t = Time (s)
- Distance -
d = d0 + v0t + 1/2at^2
d = distance (m)
d0 = initial distance (m)
v0 = initial velocity (m/s)
t = time (s)
a = acceleration (m/s/s)
Trigonometry
sin0 = o/h
cos0 = a/h
tan0 = o/a
Compressed Gas Rockets
- Kinetic Energy of escaping gas -
KE = a v^3 t d/2
KE = Kinetic Energy in Joules
a = cross sectional area of opening in m^2
v = Velocity of escaping gas in m/s
d = density in kg/m^3
t = time in seconds
- Velocity of escaping gas -
v=Sqrt(2p/d)
v = velocity in m/s
p = pressure in N/m^2
d = density in kg/m^3
CONVERSIONS
1 atm = 1.013 x 10^5 N/m^2
1 lb/in^2 = 6.90 x 10^3 N/m^2
NOTES
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If this will help, The kinetic energy of a gas with a density d under a
pressure of p escaping through an orifice with a cross section a with a
velocity of v in a time period of t is:
Magnetic Solenoids and Superconductors
- Field inside a straight, infinite, air core solenoid
-
B = n u0 i
B = Field In Teslas
n = number of turns per unit length
u0 = magnetic permeability of free space 1.26 x 10^-6 H/m (unit of length must
match n)
i = current in amps
- Magnetic Field Inside of a Solenoid (infinite)
-
B = n u i
B = Magnetic Field in Tesla
n = number of turns per unit length
u = magnetic permeability (same unit as legnth)
i = current in Amperes
- Force From Field on a Diamagnetic Material - (should
density should be part of this equation?)
F = ( X / 2 u0 ) V Bgrad^2
F = Force In Newtons
X = molecular susceptability = 1.0 x 10-5 (Chart of molecular susceptabilities)
u0 = mangetic permeability = 1.26 x 10-6 Tm/A (Chart of magnetic permeability
values)
V = Volume
B = magnetic Field in Teslas
- Current In Superconducting Coil
-
I = Vt/L
I = Current In Amps
V = Applied Voltage
t = time in seconds
L = inductance of coil in Henries
- Inductance of a Coil -
L = ( N R )^2 / (9R + 10H)
L = Inductance in mH
N = Number of turns
R = Radius of Coil in INCHES
H = Height of Coil in INCHES
Orbital Mechanics
- Gravitational Potential Energy from height
-
PEg = mgy
PEg = Gravitational Potential Energy in Joules (work that was
requried)
m = mass in kg
g = gravitational acceleration (9.8 m/s^2 for Earth) (Height will make a difference)
y = height in meters
Rocketry and Spaceflight
- Thrust -
T = mC
T = Thrust in Newtons (?)
m = propellant mass flow in kg
C = exhaust velocity in m/s
- Specific Impulse -
- "The number of seconds a pound of propellant can be used to deliver a pound of thrust and stated in terms of seconds" - Robert Zubrin, Entering Space, pg 35
- Exhaust velocity from Specific Impulse -
Mutliply the specific impulse by the earths gravitational acceleration to
get exhaust velocity
C = g (Isp)
C = Exhaust velocity in m/s
g = accleration due to gravity in m/s 9.81 m/s
Isp = Specific Impulse in seconds
- Delta V - (The 'Rocket Equation')
(M + P)/M = e^deltaV/C
M = mass of vehicle empty of propellant in kg
P = Quantity of propellant
e = 2.71828
deltaV = change in velocity in m/s
C = Specific Impule in seconds
The quantity (M + P)/M is known as the vehicle's "'mass ratio" that is, the ratio of the vehicles's weight when full of proellant to that of the vehicle empty
- "To get where you want to go in space, you generally need to change the velocity of the spacecraft from one speed and direction to another. Ths, velocity change, or deltaV, measured in units of speed, such as meters persecond (m/s), is the fundamental currency of astronautics. If you have a spacecraft with a given dry mass M (i.e. empty of propellant), and a certain amount of propellant, P, and a rocket engine with an exhaust velocity C, the following equation, known as the "Rocket Equation," shows how big a deltaV the system can generate:" - Robert Zubrin, Entering Space, pg 36
Electromagnetism
- Electric fields -
F = K Q1 Q2 / D2
F = force in Newtons
K = 8.99 x 10^9 Nm^2/C^2
Q1 = 1st charge in Coloumbs
Q2 = 2nd charge in Coloumbs
D = distance in meters
Q = CV
Q = Charge in Coloumbs
C = Capacitance in Farads - capacitor geometry and by the kind of dielectric
between
V = Voltage