In fact we often talk about trim tab position in terms of trim-speed - for a given trim tab position the speed at which the aircraft flies straight and level hands-off (i.e. zero yoke force). Once you’re past trimmed for a particular airspeed it takes a push or pull to fly the airplane at a different airspeed. In other words it’s how far from trim speed that you’re flying that determines the force.
You’ve probably also experienced trim changes on raising or lowering the flaps, and on increasing or decreasing the throttle setting. So another two yoke force factors are flap setting and power.
One factor that you may not have thought about is g-loading. It turns out that if you want to pull g (or push g) in an airplane you automatically have to pull (or push) on the yoke even if everything else - power, flaps, airspeed - stays the same.
In fact test pilots measure and talk about the “stick force per g” of an aircraft. The amount of push or pull varies proportionally with the g-force 1. For a Cessna 150 this is about 19lbs per g, and for a Cessna 182 it’s about three times that. This has everything to do with how heavy an aircraft feels to fly: an aerobatic plane will be designed with a low stick-force per g so it’s easy to fling around the sky. A jet transport has to have a very high stick-force per g so the pilots don’t throw the passengers around without thinking.
Stick force per g is controlled how the elevators are designed and has nothing at all to do with the actual weight of the aircraft, but that’s another story.
Rate of Climb and Descent
One thing that doesn’t directly affect yoke force is (unfortunately) rate of climb or descent. That’s unfortunate because climbing or descending is something we do want precise control over: it would be nice if pushing just “so” hard always made the airplane descend at a particular rate, or pulling “so” hard always made the airplane climb at a particular rate.
However life’s not like that. How hard we have to push or pull is determined directly only by the things we’ve discussed. You can’t sense how fast (or even whether) you’re going up or down only by knowing how hard you’re pushing or pulling on the yoke.
So to summarize, the amount of push or pull you need to apply on the yoke at any give time can be written like this:
Now let’s look at two examples of flight manoeuvres through the lens of the yoke forces needed to make them happen.
Example 1 - Leveling Off from a Climb
The first example is levelling off from a climb. Let’s say we’re in a Cessna 172 climbing at 80 knots at 500 fpm, trimmed for no yoke force in the climb, and we want to transition to level flight and accelerate to 100 knots.
To change from a steady climb to level flight involves a change in vertical speed, which means a vertical acceleration, which we can only do with a short-lived change in g-load. A smallish, brief g-load, and therefore only a small brief amount of force on the yoke. So the first control input we need to make is to push forward on the yoke (which lowers the nose, generating a small amount of reduced g-load) and then relax and stop pushing.
That’s the easy bit.
Now the aircraft is flying level but still only at 80 knots. We haven’t reduced power yet so the aircraft accelerates beyond its previous 80 knot trim speed. That means to stay in level flight we need to begin to apply an increasing yoke force forward. If we don’t, then the aircraft will automatically start to return to the nose high attitude it had before, briefly pulling positive g, and start to climb again. That would be the start of what’s called a phugoid oscillation.
So we push forward on the yoke to hold the aircraft off its trim speed, harder and harder as the speed builds up. (Reading this, the experienced pilot will be unconsciously reaching under the table for a trim wheel to roll in some forward trim to help him or herself maintain altitude!)
Eventually the airspeed approaches the desired 100 knots and the pilot can reduce the power to a setting to maintain that speed. Then a trim adjustment takes care of the net yoke force resulting from the new speed and power combination to make the yoke force zero for hands-off steady flight.
If we drew a graph of the force applied to the yoke against time we might see something like this:
Between A and B we push forward to lower the nose (reduced g). The push has stopped by B! Then at C we start pushing again as the speed starts to build up. At D we reduce power and put in forward trim to increase the trim
speed, reducing the force on the yoke to zero again.
Firstly the pushover at the top of the climb was much gentler, so less change in g was noticed by the passengers, giving them a more comfortable ride.
Of course it took a little longer so the pilot had to exercise better judgment to anticipate the level-off a little earlier.
Secondly the pilot rolled in some forward trim on two (or more) occasions as the aircraft accelerated, before reducing the power and giving a final trim at D. The maximum force the pilot ever had to exert was much less, in fact the whole manoeuvre could probably have been flown with just two fingers.
Example 2 - Spiral Dive
As a second example of considering yoke forces let’s talk about the spiral dive. Contrary to public opinion a spiral dive isn’t always a case of roll to some crazy bank angle, add power and point the nose at the ground. If you try exactly that - and then let go of the yoke and wait about 10 long seconds - you’ll find the airplane, unassisted by you, will go a long way towards rescuing you from the manoeuvre: as the speed builds up you’ll find the nose rises and the aircraft rolls out of the bank - another example of a phugoid oscillation.
To be fair your job as the pilot is to be able to recover from that situation faster than the aircraft rescues itself. But there is a spiral dive situation from which the aircraft won’t recover, and it’s the one you need to keep an eye open for.
If you recall, two of the yoke-force factors are g-load, and when the airspeed differs from the trim speed. To pull g you need to pull back on the yoke; and to fly faster than trim speed you need to push forward on the yoke. It follows therefore that there’s a combination of these two factors where the need to pull to create g exactly cancels out the need to push to fly faster than trim speed. That’s what happens in a stable spiral dive.
So an aircraft that’s trimmed for level flight at 100 knots is automatically trimmed for (say) 140 knots while pulling 1.4g, just like it does in a 45 degree banked turn. Or maybe 170 knots in a 60 degree bank, pulling 2g. Or 190 knots in a 70 degree banked turn pulling 3g.
Now consider the increase in drag between 100 knots and 140 knots - it's significant. In order to pay off the extra drag without an increase in engine power the aircraft has to trade in height energy - by descending, potentially quite rapidly.
A final key to the development of a real spiral dive is to realize that light airplanes have a slight amount of roll instability. At very small bank angles the wings will self-level if they’re disturbed by a tiny bit of turbulent air, but once a light aircraft has rolled beyond a few degrees of bank, unless the pilot deliberately levels the wings with an aileron input the bank angle will slowly increase. As it increases the aircraft begins to turn in the direction of the bank. As it turns, it pulls g. An increase in g without a deliberate pull-back on the yoke by the pilot is balanced out by having the aircraft fly faster than its trim speed, so the aircraft accelerates. As it accelerates the drag increases, which, without an increase in power setting has to be paid for by losing height - so the aircraft descends.
A typical Cessna 172 becomes roll stable again once it reaches about a 45 degree angle of bank. On its own, it won’t roll much past that point, but by then it has established itself in a nose down steep turn attitude, descending reasonably quickly. Unless you the pilot notice in time and fix it, you’re going to fly in to the ground.
A Real Life Example
If you’re wondering whether this has ever happened, the answer is yes. At 4:30am on 1 September 2008 a Cessna 172 crashed near Shelburne, Ontario 3. One person died, and two were injured.
The report states “The aeroplane struck the ground on an easterly heading, approximately 45º right bank, pitch angle 7º to 8º nose down, airspeed 140 knots. “, and concludes “Due to fatigue, the pilot involuntarily fell asleep resulting in the aeroplane continuing to fly in its trimmed condition until it struck the ground.” !
Trim and Yoke force... thinking about it, understanding it, and mastering it could save your life.
Becoming comfortable with and intuitively understanding what you’re feeling and doing when you push and pull on the yoke of whatever airplane you’re flying will help you become a better pilot.