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mathshit.txt
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Formulas and Constants for Atmospheric Properties Calculation
1. Temperature at Altitude (ISA model):
T = T0 - L * altitude
Where:
- T is the temperature at the given altitude.
- T0 is the sea level temperature (288.15 K).
- L is the temperature lapse rate (0.0065 K/m).
- altitude is the input altitude.
2. Pressure at Altitude (ISA model):
P = P0 * (1 - L * altitude / T0)^(g / (L * R))
Where:
- P is the pressure at the given altitude.
- P0 is the sea level pressure (101325 Pa).
- L is the temperature lapse rate (0.0065 K/m).
- g is the acceleration due to gravity (9.8 m/s²).
- R is the molar gas constant (8.314462 J/(mol·K)).
- altitude is the input altitude.
3. Density at Altitude (Ideal Gas Law):
ρ = (P * M) / (R * T)
Where:
- ρ is the density at the given altitude.
- P is the pressure at the given altitude.
- M is the molar mass of Earth's air (0.0289644 kg/mol).
- R is the molar gas constant (8.314462 J/(mol·K)).
- T is the temperature at the given altitude.
Constants:
- Sea level temperature (T0): 288.15 K
- Temperature lapse rate (L): 0.0065 K/m
- Sea level pressure (P0): 101325 Pa
- Acceleration due to gravity (g): 9.8 m/s²
- Molar gas constant (R): 8.314462 J/(mol·K)
- Molar mass of Earth's air (M): 0.0289644 kg/mol
Buoyant Force Calculation for Hydrogen Gas
Formula:
F_buoyant = ρ_fluid * V_displaced * g
Where:
- F_buoyant is the buoyant force (lifting force),
- ρ_fluid is the density of the fluid (hydrogen gas),
- V_displaced is the volume of the fluid displaced by the object,
- g is the acceleration due to gravity (approximately 9.8 m/s²).
For Hydrogen Gas:
- Density of Hydrogen (at STP): 0.08988 kg/m³
Buoyant Force Formula for Hydrogen Gas:
F_buoyant = Density_of_Hydrogen * Volume_of_Hydrogen * g
Note: Use consistent units for the calculation. If the volume is given in cubic meters, the density in kg/m³, and gravity in m/s², the result will be in Newtons (N), which is the unit of force.
FB = (ρair - ρgas) × g × V
(1.292 - 0.090) kg/m3 = 1.202 kg/m3
1 m3 × 1.202 kg/m3 × 9.8 N/kg= 11.8 N <- In the Amiga version you could just precalculate this figure and then just read from a table or something.
That formula looks like:
HL = V * 1.202 * 9.81
HL = Hydrogen lift in Newtons
V = Volume in Cubic meters
1.202 = Lifting capicity of hydrogen (1.202 KG per m3 of Hydrogen)
9.81 = Gravity
Newtons of an object is N = gravity * mass
Acceleration with Buoyant Force:
1. Calculate Gravitational Force:
F_gravity = m * g
where:
- m is the mass of the object
- g is the acceleration due to gravity (approx. 9.8 m/s^2 on Earth)
2. Calculate Buoyant Force:
F_buoyant = ρ * V * g
where:
- ρ is the density of the fluid
- V is the volume of fluid displaced by the object
If the object is fully submerged:
V = m / ρ_object
where ρ_object is the density of the object
3. Determine Net Force:
F_net = F_buoyant - F_gravity
4. Calculate Acceleration:
a = F_net / m
v = a * time
Current Airship is loosely based on LZ-127 Graf Zeppelin & the USS Los Angles
Length: 236.6 m (776 ft 3 in)
Diameter: 30.5 m (100 ft 1 in) maximum
Fineness ratio: 7.25
Height: 33.5 m (109 ft 11 in)
Drag Coefficent (USS Los Angles): 0.023
Propeller Thrust Calculation Formulas:
1. Basic Thrust Formula:
T = η * ρ * A * V * (V - V₀)
Where:
- T is the thrust,
- η is the propeller efficiency (0.7 to 0.9),
- ρ is the air density,
- A is the disc area swept by the propeller,
- V is the effective airspeed,
- V₀ is the airspeed of the aircraft (if any) in still air.
2. Disc Area (\(A\)) Calculation for Two-Bladed Propeller:
A = π * (D/2)^2 (Area of a circle)
3. Disc Area (\(A\)) Calculation for Three-Bladed Propeller:
A = (sqrt(3) * π * D²) / 4
Where:
- D is the diameter of the propeller.
OR sue the more correct formula
F = 0.5 * rho * A * (Ve^2 - V0^2)
Where:
F is the thrust (force) in Newtons
rho is the air density in kilograms per cubic meter (kg/m³)
A is the propeller disk area in square meters (m²)
Ve is the exit velocity of the air behind the propeller in meters per second (m/s)
V0 is the inflow velocity of the air entering the propeller in meters per second (m/s)
Engine Data
Fuel flow:
100% = 19 Gallons per Hour
50% = 8 Gallons per Hour
Idle = 0.5 Gallons per Hour
Fuel mass is 0.719KG per Litre
**Converting Masses**
Just devide the mass by 1000 for big things and maybe a 100 for little things like ammo
Websites:
Pressure: https://www.mide.com/air-pressure-at-altitude-calculator
Denisty: https://www.calctool.org/atmospheric-thermodynamics/air-density
Barometric Formula: https://en.wikipedia.org/wiki/Barometric_formula
Hydrogen Calculator: https://calculator.academy/hydrogen-lift-calculator/
Lifting Gas Formula: https://en.wikipedia.org/wiki/Lifting_gas#:~:text=Therefore%2C%20the%20amount%20of%20mass,m3%20%3D%201.202%20kg%2Fm&text=and%20the%20buoyant%20force%20for,9.8%20N%2Fkg%3D%2011.8%20N
ICA Wiki: https://en.wikipedia.org/wiki/International_Standard_Atmosphere#ICAO_Standard_Atmosphere
Engine Manual: https://www.lycoming.com/sites/default/files/attachments/O%2520%2526%2520IO-540%2520Oper%2520Manual%252060297-10.pdf
Fuel Calculator: https://e6bx.com/unit-converter/fuel/
Weapons Database: https://weaponsystems.net/
105mm M1 Shell: https://arconpartners.net/products/ammunition/large-caliber/105-mm-round-with-he-m1-projectile-and-m67-propelling-charge-he-for-105-mm-howitzers/