First, an ordinary HSI doesn’t contain digital logic to decide anything. Unlike an FMS or flight director, it no more tells a pilot where to go than a $5 compass recommends a direction to a disoriented hiker. Both simply present a display that informs the user of the situation. Even the full name - Horizontal Situation Indicator - implies those same limitations.
Next, if you think that in your scenario a left turn is the best method to get established on an easterly course of 090 from a navaid, then I propose we have a friendly imaginary race to demonstrate why that might not be the best choice.
We will run 2 heats. You will turn left while I turn right. We agree to perform standard rate turns, and fly at precisely the same airspeed.
Here are the objectives:
- Heat 1: Be the first to cross the 090 radial.
- Heat 2: Be the first to reach the 090 at 20 DME. (I must make the initial turn at least 180 degrees to mirror your turn)
I will describe the results, and offer an illustration. Ready? OK, here goes…
Heat #1: You have already figured yourself correctly to be the winner because you have less turn to perform. Not 5 degrees less, but 10 degrees – you turn 175 degrees left to 180, I turn 185 degrees right to the same heading. Your margin of victory, however, is miniscule. A standard rate turn is 3 degrees per second, so I would spend just over three seconds more than you turning. But because we are heading in generally the same direction as we both initiate and complete our turns, the actual margin is much less. (the angular change doesn’t equal forward speed) Anyway, the victory is well within the margin of error and exceeds either of our abilities to control flight parameters well enough for consistent results. (as well as my ability to actually compute it!)
Heat #2: I’m providing an illustration for this one because this is where it really makes a difference. Because our objective is never just to get to a radial, we must consider our actions in the context of where we intend to go after we intercept. As you can see, I beat you soundly by a margin of 4 times the radius of turn. We could calculate a distance, but we don’t need to – at a standard rate of turn I will have beaten you by 2 full minutes.
Note: I just realized that 4xRadius is correct, but not 2 minutes. Because the 2 minutes spent turning in opposite directions was along an arc. Pi is probably needed here, but it’s getting too late to think on it and make a correction right now.
Reality: I would either make a right turn and proceed direct to the fix, or set up for an angle that will get me on the radial expeditiously, while not sacrificing downrange travel towards the destination. Because the real goal is to get to your destination in the most direct and efficient manner, you should generally always plan a turn in the direction of travel. Intercepting a radial is just one means to the end, and turning the opposite way to save a few seconds of turn will cost you way more in distance traveled in the wrong direction.
Angles between 20 and 45 degrees seem to be the best compromise for intercepting.