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This applies to the Airbus 320 or Boeing 737, among others:

Although it is useless on ground, the radar altimeter will repeatedly display a value (including negative) for a specific runway and airport on the PFD.

Why would a certain runway position be -4 radar altitude as opposed to 0?

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    $\begingroup$ Good question - welcome to Av.SE! $\endgroup$ – Ralph J Jun 2 at 15:22
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The zero reading is calibrated for main-wheel touchdown in a landing attitude. With the antenna forward of the main gear, it is, at that point, higher than it will be after the nosewheel is lowered to the runway.

So to put some rough numbers to that, in the landing attitude, mains on the ground, the antenna is roughly 8 feet above the runway, but it reads 0 -- a bias of -8 feet is applied to the display as compared to the measured value. With all wheels on the ground, the antenna is about 4 feet above the pavement (about that on the 737, a bit more on the A320 with its taller landing gear). Now, the bias of -8 gives the display value of -4 (i.e. 4' above pavement + -8' bias = -4' displayed).

Addressing issues mentioned in comments: Putting the antenna directly between the main gear would be difficult on a 737 because as the wheels retract inward, there isn't a lot of space between them. I'd suspect that as far as places go to mount an antenna, right there isn't a great one just because of all the dirt & hydraulic fluid & general grime in and around the wheel wells. Somewhat forward, where everything inside the aircraft (i.e. everything except the external structure of the antenna) is sealed off from all dirt & such is probably lots better for the longevity of sensitive electronics.

Also, even mounting an antenna directly in line with the gear wouldn't remove the need for a bias... it's still 4' or so off the ground when the wheels touch and you want a displayed "0". You'd just get rid of the effect that the displayed value goes slightly negative as the nose comes down.

As I understand the system, the rad alt beam isn't all that directional... if the deck angle is +10 degrees, the measured distance is the vertical distance from the antenna to the ground - not the distance of the (hypotenuse) line 10 degrees forward of vertical. You'd get the latter with a laser pointer aimed "straight down" from the aircraft, but the rad alt just transmits a pulse, and the first return it gets (i.e. from the nearest surface, irrespective of relative angle) is what's used to compute the height.

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    $\begingroup$ Absolutely, they are. In the flare, I can read the radar altimeter digital values in the heads-up display, and as it counts down from 1 to 0, the main wheels touch. $\endgroup$ – Ralph J Jun 2 at 16:02
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    $\begingroup$ @rclocher3 Note that radar altimeters get more accurate the closer you are to the ground. You won't get 1 ft accuracy at 2000 ft. In fact, above 2500 ft the radar altimeter value is usually not shown at all. $\endgroup$ – Bianfable Jun 2 at 17:10
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    $\begingroup$ @rclocher3 Wait until you see what laser distance meters used in construction can do. $\endgroup$ – SomeoneSomewhereSupportsMonica Jun 3 at 0:22
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    $\begingroup$ @rclocher3 there are clever ways to electronically measure time-of-flight down around 10-100 picosecond resolution without even any really exotic components :) $\endgroup$ – hobbs Jun 3 at 2:17
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    $\begingroup$ @DarrelHoffman Yes - and a purely directional beam would show increasing height as the roll angle increases... not a desirable effect when approaching the flare, especially with a wing-low crosswind correction! $\endgroup$ – Ralph J Jun 3 at 14:30

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