I am targetting following : Design a Toy car which can carry 30 Kg object at a speed of 1 Km/Hr to a distance of 1 Km in 1 hour. Car will have wheel diameter of 15 cm.

Can some expert verify my following calculation and help....??

**A. Calculation for speed requirement **

Diameter of Car wheel = 15 cm = 15 x 10^{-2} x 10^{-3} Km = 15 x 10^{-5} Km

Perimeter of Car whee = 3.14 x 15 x 10^{-5} Km = 47 x 10^{-5} Km

i.e. when this 15 cm wheel rotates, it will cover a distance equal to 47 x 10^{-5} Km.

So how many times the wheel should rotate to cover 1 km distance. Therefore, ( 1 Km x 1 Rev ) / 47 x 10^{-5} Km = 2127.67 Rev in hour is to be made for 15 cm wheel to travel 1Km distance

i.e. 2127.67 Rev per hour = (2127.67 Rev / ( hr x 60 min /hr) = 35.46 RPM speed is required for 15 cm wheel to cover 1 Km in 1 hour .................**Veri-1**

**B. Calculation for Torque requirement **

Force = Mass x Acceleration

Acceleration = Speed / Time

We want speed of 1 km/hr and with that speed car should run 1 hour.

therefore acceleration = 1 km/(hr x hr) = 1 km / hr^{2 }= 1000 m / (3600^{2}) sec = 0.28 m / sec^{2}

Now Force = Mass x Acceleration = 30 Kg (Target weight) x 0.28 m / sec^{2 }= 8.4 Kg m/sec^{2}

i.e. 35.46 RPM speed required for 15 cm wheel dia and 8.4 Kg m/sec^{2 }force is required for moving 30 Kg object at 1 km/hr speed through a distance of 1 km in 1 hour. Then what is the torque required ?

Torque calculation = 8.4 Kg m/sec^{2 }x 15 cm x (1 m / 100 cm) = 1.26 N-m / 9.81 = 0.128 Kg - m = 0.128 Kg-m x (100 cm / m ) = 12.8 Kg-Cm Torque to be delivered.

**Summary : 12.8 Kg-Cm torque should be produced by a motor at 35.46 RPM speed required for a 15 cm dia wheel to move an object of 30 Kg at a distance of 1 Km with a speed of 1 /km/hr in 1 hours.**