Time / Distance question

[Steve]

Two aircraft one is going .78 one is going .85 they are 50 miles apart, when will the faster one catch the other.

I've figured out that they will meet about 550 miles down the road, but cant give a time unless I would know what M1.0 is equal to.

Any thoughts?

 

[mynameisjim]

How can you figure out the distance without knowing the temperature?

 

[pilotyip]

Temps?

M = speed of sound, it changes with temp. How about the one doing .78 is at 340 and the one doing .85 is at 360? Without a lot more information there is no answer.

 

[Fedora]

The Mach number is commonly used both with objects travelling at high speed in a fluid, and with high-speed fluid flows inside channels such as nozzles, diffusers or wind tunnels. As it is defined as a ratio of two speeds, it is a dimensionless number. At a temperature of 15 degrees Celsius and at sea level, Mach 1 is 340.3 m/s (1,225 km/h, 761.2 mph, or 661.7 kts) in the Earth's atmosphere. The Mach number is not a constant; it is temperature dependent. Hence in the stratosphere it remains about the same regardless of height, though the air pressure changes with height.
Since the speed of sound increases as the temperature increases, the actual speed of an object travelling at Mach 1 will depend on the fluid temperature around it. Mach number is useful because the fluid behaves in a similar way at the same Mach number. So, an aircraft travelling at Mach 1 at sea level (340.3 m/s, 1,225.08 km/h) will experience shock waves in much the same manner as when it is travelling at Mach 1 at 11,000 m (36,000 ft), even though it is travelling at 295 m/s (654.632 MPH, 1,062 km/h, 86% of its speed at sea level).

Science lesson over. I agree with the other two posters about the temperature. In your example, however, the teperature for both aircraft would be about the same, so now we're talking relatiivity.
(hence the need for "mach number technique" for traffic separation on Atlantic crossings).

Basically a mach 1 aircraft standard day would be flying 11nm/minute.
(661nm/hr/60min/nm)
.85x11=9.35nm/min
.78x11=8.58nm/min
the difference is .77nm/min (rate of gain)
divide that into your 50nm xample and you get about 65 minutes to catch up.

That workes out from a practical standpoint as I always "dead reckon" myself as 8nm/minute at .82 mach. Hope this helps you catch your buddy.

 

[Steve]

Science lesson over. I agree with the other two posters about the temperature. In your example, however, the teperature for both aircraft would be about the same, so now we're talking relatiivity.
(hence the need for "mach number technique" for traffic separation on Atlantic crossings).

Basically a mach 1 aircraft standard day would be flying 11nm/minute.
(661nm/hr/60min/nm)
.85x11=9.35nm/min
.78x11=8.58nm/min
the difference is .77nm/min (rate of gain)
divide that into your 50nm xample and you get about 65 minutes to catch up.

That workes out from a practical standpoint as I always "dead reckon" myself as 8nm/minute at .82 mach. Hope this helps you catch your buddy.

Thanks Fedora, thats what I was looking for.