From: dlevy@viper.engin.umich.edu (David W Levy)
Subject: Re: climbing high with a fixed pitch prop
Date: Wed, 07 Oct 92 10:17:41 EDT
Organization: University of Michigan Aerospace Engineering, Ann Arbor
Originator: dlevy@viper.engin.umich.edu


In article <1992Oct6.131805.27030@uvm.edu>, braner@trantor.emba.uvm.edu (Moshe Braner) writes:
> [please post articles relating to basic training in r.a.STUDENTS!]
> 
> Somebody at the NEFI suggested to me an unusual technique for climbing
> in a simple airplane (e.g. my 172):  accelerate to cruise speed in level
> flight, zoom up gaining altitude quickly until speed drops to about Vx,
> repeat.  I've tried that and it sure is fun, but does it really increase
> the overall climb rate?  I see two related theoretical considerations:
> 
> *	With a fixed pitch prop, more power can be delivered from the
> 	engine at airspeeds closer to cruise.  When climbing high, Vy
> 	goes down (closer to Vx) and at that low speed power output
> 	is reduced due to low engine RPMs.  (But it still is Vy!)
> 
> *	When accelerating to near cruise speed, drag goes up, which
> 	counteracts some of the increased power output.
> 
> So what's the total outcome?  I would also like to know how much would a
> "climb" (lower pitched) prop would increase climb rate at altitude, and
> ceiling?  Would one climb at a lower or higher IAS with such a prop?  And
> how much would cruise speed and fuel consumption suffer?
> 
> -- 
The basic equation for rate of climb, ROC, at constant true airspeed is:

                      Pavail - Preq
           ROC  =    ---------------
                            W

     Where: Pavail = Power Available = np * SHP
            np     = Propeller efficiency
            SHP    = Shaft Horsepower

            Preq   = Power Required = Drag*True Airspeed
            W      = Gross Weight

So ROC is a maximum for a given weight when Pavail - Preq is a maximum.
The main difference between the climb, cruise, and constant speed props
is how efficiency varies with speed.  Typical characteristics might look
like:

                  |                                                
                  |                  * * + +                       
         np       |               *    + *   +                     
                  |             *    +    *   +                    
                  |           *    +       *   +                   
                  |          *    +         *   +                  
                  |         *    +          *   +                  
                  |        *    +                                  
                  |       *    +                                   
                  |      *    +             One RPM                
                  |      *    +                                    
                  |     *    +              *  Climb Prop          
                  |     *    +              +  Cruise Prop         
                  |    *    +                                       
                  _______________________________________________

                                                            V

So, the climb prop has its best efficiency at a lower speed than the cruise
prop.  The Power available and required curves will look like:

                  |                *  *+  +        .              
                  |    Pavail   *   +    *  *  +   .                
         Pavail   |          *   +            *  +                 
           &      |        *   +                *  +              
         Preq     |       *   +                .  *  +             
                  |      *   +                .                     
                  |                         .                      
                  |                        .                         
                  |      .               .         One RPM           
                  |       .            .                                
                  |         .        .            *  Climb Prop         
                  |            . .                +  Cruise Prop       
                  |      Preq                                      
                  |                                                
                  _______________________________________________

                                                            V

(Uggh, I hate ascii graphs).
The power required is the same, but the cruise prop peaks at a higher speed,
so the speed for best rate of climb will be slightly higher.

To answer your initial question,  you will lose out when you accelerate to
cruise speed for two reasons.  First, at higher speed the power required
increases very quickly.  Second, at cruise speed you will lose some
efficiency. (Cruise props do not have their maximum efficiency at cruise
or the climb performance would suffer too much).

The end result is that, with a climb prop, you want to climb at a steady
speed somewhat lower than if a cruise prop were installed.  The exact
changes in ROC and cruise speed will depend on the prop (anybody have
example numbers?).
Xref: sparky rec.aviation.piloting:80 rec.aviation.ifr:43 rec.aviation.soaring:50