There three main aircraft types with categories of 2 to 4 person roadable flying cars, 6 to 10 person stretched (limo or SUV style) roadable flying cars and 10 to 100+ person wide flying wing bodies.

**Vertical Aircraft Types**

The VF2C is a performance flying car. It contains the same size Split Power Engine as the 4 and 8 seat versions. Although the Split Power Engine is overall one engine, it is fundamentally comprised of numerous engines called Torquers. If all of the Torquers are installed in the VF2C, there will be 28 “micro” engines. 14 for the top clockwise rotating engine and 14 for the bottom counter clockwise rotating engine. For the VF2C all of the Torquers do not need to be installed but if high g-turns and more performance is desired then more Torquers should be installed.

**Mathematics of Flight**

Mathematics governs all things. Before a skyscraper is physically built, it is built mathematically through physics formulas and geometry. As long as the dimensions and placement of parts in conjunction with known and anticipated forces are correctly applied, the building will stand and withstand. The same goes for machinery and gases. Many of the current flying car, air taxi companies place performance specs next to their renderings and prototypes. These are hoped for performances because many of these specifications do not take into account the several different forces that will act upon the aircraft and thus the engine. So although their aircrafts may get off the ground, safe and practical flight will remain a challenge. These forces range from turning and maneuvering g-forces, vertical acceleration, horizontal acceleration, wind and reduced fan thrust due to altitude or change in air density.

**VF2C**seats: 2

width: 6.5 feet

width w/ nacelles extended: 12.5 feet

length: 18 feet

gross weight: 5,000 lbs

g-forces/acceleration: 5,000 lbs (1 g) (2 g’s total)

engine torque: 10,000 lbs

fan diameter: 2’-10”, (34 inches)

fan area: 6.3 sq-ft

number of vertical fans: 4

total fan area: 25.2 sq-ft

loading per fan: 2,500 lbs

fan loading per sq ft: 397 lbs

rpm:

engine power:

propulsion fans: 2 internal (2 external optional)

**VF4C**vertical flyer four seat car

width: 6.5

width w/ nacelles extended: 12.5 feet

length: 21 feet

seats: 4

weight: 7,000 lbs

g-forces/acceleration: 5,000 lbs (.7 g’s) (1.7 g’s total)

engine torque: 12,000 lbs

fan diameter: 2’-10”, (34 inches)

fan area: 6.3 sq-ft

number of fans: 6

total fan area: 37.8 sq-ft

loading per fan: 2,000 lbs

fan loading per sq ft: 317 lbs

rpm:

engine power:

propulsion fans: 2 internal + 2 external

**VF8Cvertical flyer eight seat car**

seats: 8

width: 6.5 feet

width w/ nacelles extended: 12.5 feet

length: 27 feet

weight: 10,000 lbs

g-forces/acceleration: 5,000 lbs (.5 g’s) (1.5 g’s total)

engine torque: 15,000 lbs

vertical fan diameter: 2’-10”, (34 inches)

vertical fan area: 6.3 sq-ft

number of vertical fans: 10

total vertical fan area: 63 sq-ft

torque loading per fan: 1,500 lbs

fan torque loading per sq ft: 238 lbs

rpm:

engine power:

propulsion fans: 2 internal + 2 external

**VFWB100vertical flying wing body 100 seats**

seats: 100

private suites: 10 (1 to 2 persons per suite)

total passengers: 120

cabin body width: 55 feet

total width w/ fans: 82 feet

length: 100 feet

weight: 150,000 lbs

g-forces/acceleration: 50,000 lbs (.33 g’s)

required engine torque: 200,000 ft- lbs

vertical fan diameter: 12 feet

area per vertical fan: 113 sq-ft

number of vertical fans: 8

total vertical fan area: 904 sq-ft

torque loading per fan: 25,000 lbs

fan torque loading per sq ft: 221 lbs

engine rpm:

engine power:

propulsion fans: 2 (2 external optional)

**Designing a Vertical Flyer**

In the specifications above, the unknown parameter is fan/engine RPM (revolutions per minute). Since torque is known, then finding the RPM will allow the horsepower to be found using the equation Horsepower = Torque x RPM / 5252. In order to find RPM, the altitude must be known in order to find the air density, and the angle of attack of the variable fan blades which will give the CL or coefficient of lift factor.

**Aircraft: VF2C****Vertical Lift - capacity**

Step 1: Determine max aircraft altitude. **10,000 feet**

Step 2: Find air density. At 70 degrees Fahrenheit at sea level, air density is 14.7 psi. 40 deg. at 10,000 ft = 10.1 psi or **.00175 slugs/cubic-ft **

Step 3: Determine weight of air car. **5,000 pounds**

Step 4: Estimate g-forces from turns, passenger movement, air density change, overloading and weather. **5,000 pounds**

Step 5: Add weight and g-forces together for required engine torque. **10,000 foot-pounds**

Step 6: Determine diameter and radius of fan. **33 inch diameter, 16.5 inch radius**

Step 7: Determine area of fan. pi x radius squared = 3.14159 x 16.5^2 = **855.297 sq-in**

Step 8: Determine center hub area of fan. 3.5 inch diameter = **9.621 sq in**

Step 9: Calculate net area of fan. 855.297 - 9.621 = 845.676 divided by 144 sq in/sq-ft = **5.872 sq-ft**

Step 10: Select number of vertical lift fans. **4**

Step 11: Total fan area. Multiply net area of fan by number of fans. 4 x 5.872 = **23.488 sq-feet**

Step 12: Find max exterior width of aircraft. **6.5 feet (78 inches)**

Step 13: Find max width of engine compartment. **71 inches**

Step 14: Determine max diameter of engine. **69 inches**

Step 15: Estimate inside Torquer space width along radius. **7 inches**

Step 16: Determine rotor diameter, radius. 55 inches, **27.5 inches**

Step 17: Determine desired CL (coefficient of lift) of fan blades at 10,000 ft. 1.74 is max CL at 18 degrees angle of attach. **Cl = 1.50 at 10 degrees Note: choosing a lower CL for a higher altitude allows for more potential lift without increasing engine rpm. Step 18: Calculate air velocity: V = sqrt((2 x Lift force) / CL x air density x fan area) = 569.5 feet per second** x 720 = 410,040 in / min =

Step 19: Calculate average fan circumference. net fan area 845.676 sq-in / 2 = 422.838 sq-in + 9.621 sq-in = 432.459 sq-in. radius = sqrt (432.459/pi) = 14.705 inches. average circumference = 2 x pi x r = 2 x 3.14159 x 14.705 =

Step 20: Calculate fan rpm. air velocity / circumference. 410,040 inches/min / 92.394 inches =

Step 21: Calculate horsepower. Torque x RPM / 5252 = 10,000 ft-lbs x 4,438 rpm / 5252 =

**Vertical Lift - maximum rate of climb**

Step 1: Get mass of aircraft. 5,000 lbs = .37324 x 5,000 = **1,866.2 kilograms**

Step 2: Maximum engine torque. 10,000 ft-lbs = **44,482.22 newtons**

Step 3: Calculate maximum rate of climb. acceleration = Force / mass = 44,482.22 N / 1,866.2 kg = 23.835 meters/sec = **53.31 miles per hour = **4,691.92 feet per minute

Step 4: Select target cruise altitude. **10,000 feet**

Step 5: Calculate time. 10,000 feet /4,691.92 feet per minute= **2.13 minutesStep 6: Calculate g-force. 4,691.92 / 60 = 78.198 feet per sec / gravity 32.1740 feet per sec-sq = 2.43 g’s Horizontal Flight - minimum lift speed**Step 1: Determine width of aircraft.

Step 2: Determine length of aircraft.

Step 3: Calculate area of aircraft.

Step 4: Calculate area of nacelles. 34 x 34 = 1,156 / 144 = 8.027 sq-ft x 4 nacelles =

Step 5: Gross aircraft bottom surface area. 177 sq-ft + 32.11 sq-ft =

Step 6: Calculate minimum lift speed of aircraft at sea level. V = sqrt((2 x Lift force) / CL x air density x area) = sqrt ((2 x 5,000 lbs) / 1.0 x .00237 x 149.11) = 168.21 feet per sec /1.46 =

Step 7: Calculate minimum lift speed at 10,000 ft.

**Horizontal Flight - acceleration**

Step 1: Find mass of aircraft. 5,000 pounds =** 2,267.962 kg**

Step 2: Find available torque. Max torque minus weight of aircraft. 10,000 ft-lbs - 5,000 lbs = 5,000 lbs = **22,241 newtons**.

Step 3: Calculate max acceleration. a = F/m = 22,241 newtons/2,267.962 kg = 9.8 meters/sec = **21.922 miles per hour**

**Horizontal Flight - velocity**

Step 1: Width of aircraft. **6.5 feet**

Step 2: Height of aircraft. **3.75 feet**

Step 3: Calculate cross sectional area of aircraft. **24.375 sq-ft**

Step 4: Calculate cross sectional area of 2 nacelles. 3.5 in x 34in = 119 sq-in / 144in/sq-ft = .826 x 2 front nacelles = **1.653 sq-feet **

Step 5: Total cross sectional area. **26.028 sq-feet**

Step 6: Determine drag coefficient (equal to a sports car). **.28**

Step 7: Estimate desired top speed. **600 miles per hour**

Step 8: Calculate drag at sea level. .5 x air density x aircraft speed^2 (ft/sec) x Drag Coeff. x cross sectional area = **- 6,424 lbs is less than 10,000 ft-lb torque capacity.**

**Horizontal Flight - with wing module - minimum lift speed**

Step 1: Find area of aircraft. **117 sq-ft**

Step 2: Find width of wing. 60 inches

Step 3: Find depth of wing. at aircraft exterior 32 inches, at wing tip 12 inches.

Step 4: Calculate area of wing. area =(( 32 + 12)/2) x 60 = 1320/144 = 9.166 sq-ft x 2 = **18.33 sq-ft**

Step 5: Add area of aircraft and wing together = 117 + 18.33 =** 135.33 sq-ft**

Step 6: Determine average coefficient of lift between aircraft body and wing.** 1**

Step 7: Calculate minimum lift speed of aircraft at sea level. V = sqrt((2 x Lift force) / CL x air density x area) = sqrt ((2 x 5,000 lbs) / 1.0 x .00237 x 135.33) = 176.57 feet per sec /1.46 = **121 miles per hour**

**Engine design**

Step 1: Find circumference of rotor. rotor radius 27.5 inches, 2 x pi x r = **172.787 inches**

Step 2: Estimate desired number of Torquers per engine. **14 **

Step 3: Calculate Torquer radian width. 172.787 12 inches / 14 = **12.34 inches**

Step 4: Multiply number of Torquers by 2 (for anti-precession engine).= **14**

Step 5: Calculate moment arm to determine required virtual torque. 1+ radius 27.5 inches **3,040 lbs, 30.4% of required torqueStep 6: Determine how many simultaneously firing Torquers. 6**. 3 per engine.

Step 7: Calculate rotor force required per Torquer. 3,040 lbs / 6 Torquers =

Step 8: Determine distance between rotor edge and Torquer combustion chamber.

Step 10: estimate combustion chamber length.

Step 11: Calculate gas expansion and final required combustion force. (3 inches + 3 inches) / 3 inches = 2 x 507 = 1,014 pounds

Step 13: Calculate exit pressure from combustion chamber. 1,014 lbs / 2 sq-in =

Step 14: Calculate combustion chamber volume. pi x radius^2 x h = 3.14159 x 1^2 x 3 =

Step 15: Determine type of fuel and its combustion temperature. Octane has an adiabatic (no heat or gas mass loss) temperature of 3,880 degrees Fahrenheit, however in practice the actual useful combustion temperature is

Step 16: Determine air-fuel ratio by mass. 14.7 lbs of air to 1 lb of fuel, 6.8% fuel by mass.

Step 17: Determine desired compression ratio of air-fuel mixture by volume.

Step 18: Estimate average outside air temperature: 90 degrees F.

Calculate air temperature when compressed: P1V1/T1 = P2V2/T2 =

Fuel Consumption

Takeoff and Landing

Step 1:

Step 1: Select drag force. (form horizontal flight velocity above) - 6,424 lbs.

Fuel Consumption

Step 2: Calculate inertia of rotor.

Step 3: Find fastest combustion time for given fuel.

Step 4: Calculate inertia reduction per second when Torquer is not firing.

Step 5: Calculate time between Torquer “sets” firing.

Step 6: Divide total Torquers per engine by number of Torquers in a Torquer set.

Step 7: Calculate Torquer firing per second

Step 8: Calculate fuel consumption for second. per minute.

**Fuel Tank Size**

Step 1: Estimate desired flight distance.

Step 2:

**Flight Time**

Step 1: Determine city to city destination length.

Step 2: Determine desired flight speed.

Step 3: Calculate time.

**Financing**

Step 1: Estimate cost of aircraft.

Step 2: Estimate time length of financing in years.

Step 3. Estimate interest rate

Step 4. Determine monthly note

**Economics - for personal flying**

Step 1: Determine number of persons flying.

**Economics - for shared personal flying**

Step 1: Determine number of persons flying.

**Economics - for per trip leasing**

Step 1: Determine number of persons flying.

**Economics - for person taxi business**

Step 1: Determine number of persons flying.