Time dilation in an airplane propeller

TIME DILATION IN AN AIRPLANE PROPELLER

INTRODUCTION

Airplane Propeller is the engine that powers the airplane. The diameter of Airplane Propeller varies from 5 feet [airbus models] to 12 feet [Boeing 777]. Consider a Jumbo Jet Boeing 777 Airplane Propeller which rotates at 481 mph and an observer who is stationary with respect to the Airplane Propeller. According to the Special Theory of Relativity, the Airplane Propeller’s clock would run slower compared to the observer’s clock. We’ll find the time gained by the Airplane Propeller relative to the stationary observer.

ASSUMPTIONS

Earth is a perfect homogenous sphere.

The effect of Gravitational time dilation is negligible.

CALCULATION

The Airplane propeller velocity is,

v = 481 mph = 213.88 m/s

According to the Special Theory of Relativity, the time dilation equation is,

t' = t/γ [s]

t’ – Actual time or Airplane Propeller’s time. [s]

t - Proper time or Stationary observer’s time. [s]

γ – Relativistic gamma factor, γ = 1/√ [1-(v/c) ²]

c - Velocity of light [c = 3*10⁸ m/s]

t' = t*√ [1-(v/c) ²]

t' = t*√ [1-5.0827*10^-13]

t' = t*√ [0.999999999999492]

t' = t * 0.999999999999746

CONCLUSION

We can observe that proper and actual time isn’t the same which proves that time dilates on Airplane Propeller relative to the stationary observer. We’ll consider 2 different t’ values and calculate t value. The larger the t’ the more is the difference between t and t’. Thus in one hour the Airplane Propeller gains 0.0152 nanosecond over the observer and in 15 hours it'll gain 13.7 nanosecond. So the more the propeller rotates the better ‘cause it’ll gain more time due to time dilation by rotating rather than just staying stationary.

Time	t’ [Stationary Propeller] (s)	t [Rotating Propeller] (s)	Difference (s)
1 minute	60	59.9999999999848	0.0000000000152
1 hour	3600	3599.99999999909	0.00000000091
15 hours	54000	53999.9999999863	0.0000000137