Re: [Jsbsim-devel] C-172 Performance

[Ron F. <ron...@at...>]

----- Original Message ----- 
From: "Jon Berndt" <js...@ha...>
To: <jsb...@li...>
Sent: Tuesday, October 12, 2004 10:06 PM
Subject: RE: [Jsbsim-devel] C-172 Performance


> David wrote:
>
> > From the POH: 10 degrees flaps, break ground as soon as possible (say,
> > 45-50 kias), accelerate in ground effect, then climb out at 57 kias
> > until all obstacles cleared.  In real life, it's normal to hear to
> > stall horn when you break ground, so don't be surprised if you hear it
> > in FlightGear as well.
>
> I'll give that a try.

    Seems official rotation IAS is 52 kts (at rated weight).

    It's really hard to measure TO distance over an obstacle. Too dependent
on pilot technique.

    However, it's not so hard to find time and distance to accelerate to
rotation IAS.

    Best climb rate is near the speed where Cdi = Cdo.  Since RPM, thus P
increases at higher speeds, one can set his pitch to climb a bit faster than
the point of L/D max and climb near as fast.  Prop efficiency also drops at
lower speeds, so climbing a bit faster than at L/D max is again reasonable.
Cooling is also better at higher speeds.


> > In fact, the 172r's IO360 is a 180 hp engine, derated to 160 hp and
> > 2400 rpm; the 172p has a 160 hp O320.  In both cases, because of the
> > fixed-pitch prop the engine will develop full rated horsepower only at
> > sea level and a relatively high forward speed -- maximum static
> > horsepower will be considerably lower (i.e. you'll never see anything
> > close to maximum power from the plane when it's standing still, even
> > with full throttle).
>
> What does that mean, "derated"? Should I set the maxhp for the engine to
160 or 180?
> Jon


    AT wide open throttle, AC engines generate approximately constant torque
over a wide range of RPM's.  -

    P = w*Q, where w = 2 Pi N.

    So, P is nearly proportional to engine RPM.

     RPM has to be limited to avoid excessive engine stress.

    Note 'stock car' enginers are run much faster than they would turn in a
'off the lot' version.  And, blown engines are common. ;)

    AC engines don't blow up if RPM is higher than red line.  However,
useful life and long term reliability are reduced  if engines are run at
higher RPM.  There are subtle details such as keeping crankshaft stress
cycles below the value where fatigue damage occurs (Al fatigues with even
the smallest stress cycles).

     Fixed pitch prop diameter is critical.  I think torque varies with d^4.
FAA TCDS specs give the diameter limits for a given powerplant.  Props
shorten as tip nicks are filed off.

    Yes, the 172R simply lets the powerplant run up to 2700 RPM to get the
180 rate HP.  While the 172P uses virtually the same powerplant, but with
either a larger diameter prop, or one with a 'higher lift' blade airfoil.
This results in lower maximum RPM, thus lower maximum HP.

    As David said, one only gets rated HP at SL at IAS conditions.  And,
only when the TAS is high enough so the rated RPM is reached.


   Variable Pitch props let one set maximum rated RPM, even at zero runway
speed.  Thus, the powerplant develops rated HP at all times.   Translating
into a higher TO thrust and shorter TO distance.

    With a CS prop RPM is almost always decreased after a bit of altitude is
gained.  Especially with turbocharged powerplants.  For turbocharged
engines, Boost MP is also dropped to METO (Maximum Except for TakeOff)
value.

    At full throttle, the mixture is automatically quite rich.  To get more
cooling from fuel evaporation.  Only below 75% HP is one supposed to lean.
At higher altitudes one can always lean, since MP is limited (unless one has
a super/turbo charger).

    -----------------------------------

    It is challenging to get a good powerplant, prop, and AC drag model.
One that matches the POH tables.

    In fact, it's near impossible to get a good overall  model unless a many
of the parameters are known before hand.  If one has a good powerplant model
(one that accounts for friction, induction pressure, F/A ratio, RPM, etc.
then the two required prop Coefficients can be experimentally adjusted.
Conversely, if one has a good prop (installed, not test stand data) model,
then he can play with the powerplant details to get a reasonable fit.

    MSFS uses Ceta and Cp in its prop tables.  I know FG uses a different,
though equivalent pair.  The advantage of using Ceta is that one can adjust
prop efficiency as a function of N and J more easily than a Coefficient that
indirectly affects Ceta.     I adjust Cp to get an appropriate torque (or
power) vs RPM variation.  For a FP prop, a Cp that lets the RPM get to rated
RPM at nearly maximum SL TAS.  It's something like the Gear Ratio in a
transmission, though not exactly.

    I've started with published values for Cp and/or Ct for a typical 72"
C172 prop.  Then, made small adjustments to move performance to the poh
entries.   While I adjusted the powerplant curves from published values and
experience.

    I've set Cdo to get maximum rated speed.  Note Cdi is small at maximum
speed.  I probably set Cdi from the value originally published in the simple
FG parameter set.  I think the C172/182 airframe has an Induced Drag
Constant of 0.055 (Cdi=IDK at CL=1.0).  That induced drag is consistent with
Smetana's value; and also results in appropriate climb performance.

    Regardless, one can calculate the IDK from 1/(Pi*AR*e).  Where e is
typically 0.80 for small, high wing AC, and 0.7 (or less) for low wing AC
(such as the PA-28).

    Note: few C172's hit the maximum poh speeds.  A more realistic model
might be based on 5 kts slower maximum TAS.

    I have scans of at least one C172 PoH.

    Ron