What is the slant range error for an aircraft flying at 9000 feet absolute altitude above a DME located at elevation 2000 ft, when the slant range is 12 NM?
A)0,09 NM.
B)0,57 NM.
C)1,42 NM.
D)0,31 NM.
The difference between slant range and true horizontal range can be tested using the following equation:
True Range = √(Slant Range squared – Aircraft Height squared)
The wording of the question is rather curious in that it states that the “an aircraft at 9000 feet absolute altitude above a DME located at 2000 feet elevation”. This should be interpreted as meaning that the height of the aircraft is 9000 feet above the DME.
Multiplying by 1 nm / 6080 feet converts the 9000 feet into 1.48 nm
With the aircraft at 1.48 nm above the DME at slant range of 12 nm we have the following:
True Range = √(Slant Range squared – Aircraft Height squared)
True Range = √(12 nm squared – 1.48 nm squared) = 11.91.
So the slant range is 12 nm and the true range is 11.91 nm, giving an error of 0.09 nm.
An aircraft flying at flight level 250 wishes to interrogate a DME beacon situated 400 ft above mean sea level.
What is the maximum range likely to be achieved?
A)198 nm.
B)222 nm.
C)175 nm.
D)210 nm.
Because radio waves travel in straight lines, the maximum range of DME is limited by the height of the aeroplane, the height of the transmitter and the curvature of the earth.
Maximum range can be calculated using the standard equation:
Max range = 1.25 x (√ aircraft height + √ ground station height)
The aircraft is at FL250 which is 25000 feet.
The DME ground station is at 400 feet so:
Max range = 1.25 x (√ 25000 ft + √ 400 ft) = 222.64 nm.
The closest option is 222 nm.
Last edited by keith williams; 18th Apr 2012 at 13:33.