Time dilation in Concorde Airplane

TIME DILATION IN CONCORDE AIRPLANE

INTRODUCTION

Concorde was a French Commercial airliner which was capable of traveling at supersonic speeds. The Concorde had a top speed of 2.04 Mach. Consider an observer in Concorde who travels from destination A to B and another observer who is stationary with respect to the Concorde. According to the Special Theory of Relativity, the Concorde’s clock would run slower compared to the observer’s clock. We’ll find the time gained by the Concorde relative to the stationary observer.

ASSUMPTION

The effect of Gravitational time dilation is negligible.

CALCULATION

The Concorde’s velocity is,

v = 2.04 Mach = 605.27 m/s

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

t' = t/γ [s]

t’ – Actual time or Concorde’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*√ [1-4.0705*10^-12]

t' = t*√ [0.999999999995929]

t' = t* 0.999999999997965

CONCLUSION

We can observe that proper and actual time isn’t the same which proves that time dilates on Concorde relative to the stationary observer. We’ll consider 3 different t’ values and calculate t value. The larger the t’ the more is the difference between t and t’. Thus the Concorde gains 7.33nanosecond in 1 hour and 51.3nanosecond in 7 hours over the stationary observer. 

Time	t’ [Stationary observer] (s)	t [Observer in Concorde] (s)	Difference (s)
1 minute	60	59.9999999998779	0.0000000001221
1 hour	3600	3599.99999999267	0.00000000733
7 hours	25200	25199.9999999487	0.0000000513