BnZs you’re focused on power-to-weight, best rate of climb, & top level speed. Before we discuss your AH flight tests these concepts need to be cleared up. They are the basis for your premise of zoom climb performance and your logic runs into trouble first here.
Aerodynamic figures of merit (FOM) like L/D, P/W (power-to-weight), T/W, CD (drag coefficient), S/W (wing-loading), etc. give us some indication of an airplane’s performance. Figures of merit are often used for their simplicity. Their simplicity is also their danger because simplification abstracts and hides the complexities underneath. The key is understanding what a FOM means and applying it in the right context. Because they are simple it’s easy for people to use them to make erroneous conclusions about an aircraft’s performance because they misapply the FOM, usually in the form of over-simplification.
Precautions with Aerodynamic Figures of MeritTake lift-to-drag ratio (L/D) for instance. Quoting Dr. Warren Phillips,(
Mechanics of Flight) “This maximum value for L/D is often referred to simply as the lift-to-drag ratio for the aircraft. For example, you may hear it said that a particular airplane has a lift-to-drag ratio of 12.
This manner of speaking could erroneously lead the student to believe that this airplane will always produce 1 pound of drag for each 12 pounds of aircraft weight. Nothing could be further from the truth...the ratio of lift to drag for an airplane varies greatly with airspeed. It must be remembered that when an aerodynamicist specifies an unqualified lift-to-drag ratio for an aircraft, he or she is referring to the maximum lift-to-drag ratio for that aircraft”. (Bold emphasis added).
Conceptually Dr. Phillips’ warning applies for other aerodynamic figures of merit, in our case power-to-weight related to climb performance. We can’t assume key aero variables and thus figures of merit stay fixed, nor do they remain fixed relative to one airplane to another. Thrust, drag, and power all change with changing velocity, altitude and configuration.
Power-to-Weight Ratio & Climb PerformanceLet’s focus on power-to-weight ratio since this is important for us. You’ll hear that climb performance is a function of airplane power-to-weight ratio but you have to understand what all that means.
- First, to be precise it’s actually excess-power-to weight ratio that determines rate of climb performance. Excess-power-to-weight ratio is NOT = engine-HP/weight (more on this later). Excess-power-to-weight ratio, otherwise known as Specific Excess Power (Ps) is:
Ps = (Thrust– Drag)*Velocity / Weight
- Second just like L/D ratio Ps varies with respect to other things. The value of Ps changes when velocity, altitude, or weight changes. Just like L/D ratio, Ps does not remain constant across the full flight envelope of an airplane.
- Third best rate of climb performance occurs at the maximum excess-power-to-weight ratio for a propeller plane. (Best rate of climb usually means best STEADY rate of climb, or in other words when an airplane climbs at a constant velocity.) All this implies that maximum Ps for the best steady rate of climb occurs only at a specific point in the flight envelope.
Let’s use an example to illustrate. Suppose we have Airplane A with the following specs: BHP=1000 hp, Weight=5577 lbs, Prop Diam=9 ft, CD0=.028, Wing Area (S)= 208 ft^2.
This is a graph of Plane A’s steady climb performance at sea level. In this example we’ve FIXED the altitude of the airplane (at sea level) and the weight (5577 lbs) so that we can further isolate other variables to visualize how they vary with respect to velocity. Plotted on this graph are:
Airplane Steady Rate of Climb (ft/min) – solid blue line
Airplane Power Available (HP) – dashed blue line
Airplane Power Required (HP) – dotted blue line
The rate of climb curve is nothing more than a plot of the Ps function:
Ps = (Thrust – Drag) * Velocity / Weight or,
Ps = (Thrust*Velocity – Drag*Velocity) / Weight or,
Ps=(power_available – power_required)/Weight where
Thrust*Velocity = power available
Drag*Velocity = power required
Thus climb performance is a function of excess-power-to-weight ratio. Note that the rate of climb is a curve and varies with velocity. Rate of climb = Ps = excess-power-to-weight ratio. This means excess-power-to-weight ratio varies and is not a fixed value. Infact it varies by the difference between power available and power required (Pav minus Prq) as they change with velocity: the greater the difference, the better the ROC.
In our example across the velocity envelope the engine BHP is operating at 1000 HP at full throttle. If you look at the power-available curve however you’ll notice that it is a range and not a fixed value. Also we don’t even actually hit 1000hp. For Plane A it tops out around 800hp. It’s because an airplane’s ability to convert engine BHP into power available depends on the efficiency of the propeller. The power available curve changes with velocity because propeller efficiency changes with velocity. The point is power available is not a fixed constant value. Nor is power required.
I’ve drawn a reference line through points A, B, C, & D on the graph. Plane A has a best rate of climb at 3000 fpm at the peak of the ROC curve at point C. There is only ONE velocity (point A), ONE power required (point B), and ONE power available (point D) that results in the best rate of climb at point C. Maximum steady rate of climb occurs where the difference between power available minus power required is greatest. This is represented and is validated by visual inspection of the difference in HP between points B & D compared to other parts of the graph.
When we talk about best steady rate of climb we’re really focusing on where Ps (excess-power-to-rate ratio) is at a maximum. This is essentially a single point. We’re not concerned with Ps outside of this maximum point. The AH ROC charts are just a plot of each maximum point at each altitude for a given weight. String them all together and you get the ROC chart. However they don’t tell us anything about Ps outside of maximum excess-power-to-rate ratio.
Where Does Simple Power-to-Weight Ratio for Best Steady Climb Performance Come From?If best climb performance is at maximum excess-power-to-rate ratio, where do we get this notion of using an even simpler figure of merit like “power to weight” (engine HP/ weight) from? It’s nothing more than a proxy for maximum excess-power-to-rate ratio.
Why does this simple figure of merit work as a predictor of best climb performance? Look back at our rate of climb figure. Notice that at maximum rate of climb:
Point D – power available ~700 HP
Point B – power required ~150 HP
Because at best rate of climb power_available >> power_required, as an approximation we ignore power required and drop it from the Ps equation which gives us:
Ps= ROC ~ power_available / weight
We further approximate power available = max engine BHP because power available at best rate of climb is closer to maximum rated power of the engine (For Plane A 700hp~1000hp). Applying this 2nd approximation we get:
ROC ~ engine_power / weight
So basic “power-to-weight” ratio is nothing more than a simple approximation to estimate best steady rate of climb performance. It’s actually a decent proxy for best steady rate of climb performance.
The key is that basic power-to-weight ratio is only an approximation for MAXIMUM excess-power-to-weight ratio which is only a SINGLE POINT on the Ps curve. It is not a proxy for the whole Ps curve to predict Ps over the full flight envelope. So when we use power-to-weight ratio we have to be mindful of this limitation. (There’s a 2nd limitation in that simple power-to-weight ratio is also impacted by altitude as well which is altogether another topic.). It doesn’t give us any indication of how Ps varies outside of the point of best rate of climb.
