## Physics Formulas

### Formula #1

- I = m × r2 –Inertia Formula (I = m × (r × r) M = mass, r = width/diamiter

Distance / Time = Speed

Distance / Avg. Time = Avg Speed

(Final Speed – Initial Speed) / Time = Avg. Acceleration

Gravitational acceleration = 39.24 blocks/s/s

**Hovering**

Force to maintain a hover = (Mass * 0.2616) / number of thrusters.

(Note, make sure that the average of the position of the thrusters is in line with the centre of mass, and that the distance between the centre of mass and each thruster is the same)

Force to maintain a hover with angled thruster = (Mass * 0.2616) / (cos(angle) * number of thrusters)

Slope = Rise/Run …. (speed/or/acceleration/or/distance)/Time

Formulas Horse-Power = 1.225*(number of blocks(meters) in front)*()*velocity^3

The horsepower needed to overcome aerodynamic drag at a given speed is: HP = k*A*Cd*v^3 Density of air = 1.225 kg/m³

Where HP is horsepower, k is the density of air, A the frontal (cross-sectional) area, Cd the coefficient of drag, and v the velocity. The density of air depends on conditions but is nominally .08 lb/ft^3.

Aerodynamic drag is calculated as: F = 1/2 CDAV^2

Where: F – Aerodynamic drag force, Cd – Coefficient of drag, D – Density of air (nominally about 0.08 pounds per cubic foot.. yes I know that’s not a technically accurate mass but it saves converting to and then back from metric), A – Frontal area, V – Velocity of object

To estimate engine HP from 1/4 mile run: HP = ((trapspeed/234)^3) * weight

Tire Diameter in inches = ( ( Tire Width * Aspect Ratio ) / 25.4 ) * 2 + Wheel Diameter

*Example: 245/40-17 would be ( ( 245 * .40 ) / 25.4 ) * 2 ) + 17 = 24.71653543307*

MPH = ( RPM * Tire Diameter ) / ( ( gear ratio * final drive ) * 336 )

*Example: ( 8000 * 24.71653543307 ) / ( ( .771 * 4.062 ) * 336 ) = 187.9074535627 MPH*

Of course the tires expand at high speeds so this isn’t totally accurate.

DRAG = FD = ρ*v2*CD*A/2

To find Drag Coefficent solve; formula for angular velocity is ω = (θf – θi) / t Key = ω = angular velocity θf = the final angle θi = the initial angle t = time

Angle of attack formula = atan(velocity along yaw axis/velocity along roll axis)= (answer)

**1=**

- CD ≈ 0.01*θ

Where θ is the angle of attack of the object in radians. What I don’t like about this formula is the “≈” sign, and so I avoid using it completely. to convert degrees to radians use “(degrees)/57.2957795”

**2=**

- CD = (2
*FD)/(ρ*v2*A)

Where ρ is the density of the fluid the object is travelling in, v is the velocity of the object, CD is the drag coefficient of the object and A is the surface area of the object.

Any object moving through a fluid experiences drag – the net force in the direction of flow due to pressure and shear stress forces on the surface of the object.

The drag force can be expressed as:

Fd = cd 1/2 ρ v2 A (1)

Where:

- Fd = drag force (N)
- cd = drag coefficient
- ρ = density of fluid (1.2 kg/m3 for air at NTP)
- v = flow velocity (m/s)
- A = characteristic frontal area of the body (m2)

The drag coefficient is a function of several parameters like shape of the body, Reynolds Number for the flow, Froude number, Mach Number and Roughness of the Surface.

The characteristic frontal area – A – depends on the body.

Objects drag coefficients are mostly results of experiments. The drag coefficients for some common bodies are indicated below:

Type of Object, Drag Coefficient:

- – cd – Frontal Area
- Laminar flat plate (Re=106) 0.001
- Dolphin 0.0036 wetted area
- Turbulent flat plate (Re=106) 0.005
- Subsonic Transport Aircraft 0.012
- Supersonic Fighter,M=2.5 0.016
- Streamlined body 0.04 π / 4 d2

Airplane wing, normal position 0.05 WING DRAG COEFFICENT

- Sreamlined half-body 0.09
- Long stream-lined body 0.1
- Bicycle – Streamlined Velomobile 0.12 5 ft2 (0.47 m2)
- Airplane wing, stalled 0.15
- Modern car like a Tesla model 3 or model Y 0.23
- Toyota Prius, Tesla model S 0.24 frontal area
- Tesla model X
- Sports car, sloping rear 0.2 – 0.3 frontal area
- Common car like Opel Vectra (class C) 0.29 frontal area
- Hollow semi-sphere facing stream 0.38
- Bird 0.4 frontal area
- Solid Hemisphere 0.42 π / 4 d2
- Sphere 0.5
- Saloon Car, stepped rear 0.4 – 0.5 frontal area
- Bike – Drafting behind an other cyclist 0.5 3.9 ft2 (0.36 m2)
- Convertible, open top 0.6 – 0.7 frontal area
- Bus 0.6 – 0.8 frontal area
- Old Car like a T-ford 0.7 – 0.9 frontal area
- Cube 0.8 s2
- Bike – Racing 0.88 3.9 ft2 (0.36 m2)
- Bicycle 0.9
- Tractor Trailed Truck 0.96 frontal area
- Truck 0.8 – 1.0 frontal area
- Person standing 1.0 – 1.3
- Bike – Upright Commuter 1.1 5.5 ft2 (0.51 m2)
- Thin Disk 1.1 π / 4 d2
- Solid Hemisphere flow normal to flat side 1.17 π / 4 d2
- Squared flat plate at 90 deg 1.17
- Wires and cables 1.0 – 1.3
- Person (upright position) 1.0 – 1.3
- Hollow semi-cylinder opposite stream 1.2
- Ski jumper 1.2 – 1.3
- Hollow semi-sphere opposite stream 1.42
- Passenger Train 1.8 frontal area
- Motorcycle and rider 1.8 frontal area
- Long flat plate at 90 deg 1.98
- Rectangular box 2.1

θ = angle of attack in radians

Angle of attack formula is: atan(velocity along yaw axis/velocity along roll axis) = (answer)

To convert degrees to radians use “(degrees/answer)/57.2957795”

Formula for angular velocity is ω = (θf – θi) / t Key = ω = angular velocity θf = the final angle θi = the initial angle t = time

Key = ω = angular velocity θf = the final angle θi = the initial angle t = time

t get time use formula Distance/Speed = Time

*coefficent of drag(CD) formula:

CD ≈ 0.01*θ

Overall the HorsePower needed to overpower aerodynamic drag is CoDr = Coeffectiant of Drag * or Codr = 0.01*(atan( ( (360 – 0) / (Distance/Speed) ) / ( (360 – 0) / (Distance/Speed) ) ))/57.2957795

Horse-Power = 1.225*(number of blocks(meters) in front)*(CoDr)*velocity^3

Full formula is:

Horse-Power = 1.225*(number of blocks(meters) in front)*(0.01*(atan( ( (360 – 0) / (Distance/Speed) ) / ( (360 – 0) / (Distance/Speed) ) ))/57.2957795)*velocity^3

### Formula #2

- D = .5 * Cd * r * V^2 * A

The drag equation states that drag (D)is equal to a drag coefficient (Cd) times the density of the air (r) times half of the square of the velocity (V) times the wing area (A).

To Overcome Aerodynamic drag, the formula is:

- P^d = F^d · v = ½pv^3AC^d .

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