What empirical evidence, or physics explanation validates the choice of transmitting from a valley, slope or summit?

I’m not an expert, but I’ll get the ball rolling. Perhaps someone with more expertise will come along and provide a more authoritative answer.

The takeoff angle is often defined as the angle of maximum radiation in the vertical plane, relative to the horizon. The ARRL Antenna Book calls this angle the elevation angle of the antenna. For an antenna that is directional in the horizontal plane, the takeoff angle of most interest is assumed to be measured (or computed, if dealing with a model) at the front of the antenna.

As a practical matter, such measurements (or computations) are customarily done assuming that the antenna is installed over level ground. In terms of the physics involved, it would be more accurate to define the takeoff angle relative to the average plane of the ground in the vicinity of the antenna. Why? Because the ground in the immediate vicinity of an antenna significantly influences the radiation pattern in both azimuth and elevation planes. This influence diminishes more than a few wavelengths away.

This raises the question of how one determines exactly where the ground plane lies under an actual antenna, but it makes apparent, at least qualitatively, that when an antenna is installed over sloping ground, the effective takeoff angle — relative to the horizon — is tilted by the degree of ground slope.

The first time someone raised this topic to me was at Field Day, quite a few years ago. The Field Day site was close to a mountain ridge, just a few meters from the Appalachian Trail, in fact. The mountain (more like a tall hill, if you happen to be from Colorado or Wyoming) is oriented north/south. Our site on the west side of the ridge sloped downhill at an angle of about 15 degrees.

One of our antennas was a 40 m dipole, about 30 feet off the ground, and oriented parallel to the ridge. Its theoretical takeoff angle, relative to the underlying ground plane, is in the vicinity of 60 degrees. But with the ground slope prevailing at the site, the effective takeoff angle was lowered to 45 degrees toward the west, and raised to 75 degrees toward the east.

What are the practical implications of this? The elevation pattern of a dipole situated roughly 1/4 wavelength above real ground is broad, with usable radiation over a wide range of elevation angles. During the day, with NVIS propagation dominating, a 15-degree tilt probably enhances NVIS propagation, directing more radiation straight up than would be the case over level ground. That theoretically enhances our ability to work East Coast stations out to several hundred miles. At night, when NVIS propagation is no longer available and skip conditions prevail, the 15-degree decrease in effective takeoff angle to the west marginally enhances our ability to work stations on the West Coast and beyond.

In reality, given the broadness of the dipole’s elevation pattern, the effect of the sloping ground probably isn’t great. But any influence it does have, at least in our situation, is probably net positive.

For a beam antenna, like the classic triband Yagi, the radiation is more concentrated close to the takeoff angle. Raising or lowering the effective takeoff angle by placing the antenna over sloping ground will have a more pronounced effect. Whether that effect is beneficial or not depends on the prevailing ionospheric conditions. Lower takeoff angles generally favor DX communications, but the optimum takeoff angle for communications between any two points depends on the height and density of the ionosphere at the time the communication is attempted.

In the final analysis, the slope of the ground at our Field Day site is less important than its other attributes: great views, an opportunity to chat with through-hikers on the Appalachian Trail, and cooler temperatures and less humidity, to name a few.