Return-Path: Sender: "Marvin Kaye" To: lml@lancaironline.net Date: Fri, 18 Mar 2005 20:56:41 -0500 Message-ID: X-Original-Return-Path: Received: from imo-d03.mx.aol.com ([205.188.157.35] verified) by logan.com (CommuniGate Pro SMTP 4.3c3) with ESMTP id 810913 for lml@lancaironline.net; Fri, 18 Mar 2005 20:19:34 -0500 Received-SPF: pass receiver=logan.com; client-ip=205.188.157.35; envelope-from=REHBINC@aol.com Received: from REHBINC@aol.com by imo-d03.mx.aol.com (mail_out_v37_r5.31.) id q.f6.4ca9b006 (17377) for ; Fri, 18 Mar 2005 20:18:45 -0500 (EST) From: REHBINC@aol.com X-Original-Message-ID: X-Original-Date: Fri, 18 Mar 2005 20:18:45 EST Subject: Re: [LML] Re: superchargers X-Original-To: lml@lancaironline.net MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="-----------------------------1111195125" X-Mailer: 9.0 for Windows sub 5116 -------------------------------1111195125 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Content-Language: en In a message dated 3/18/2005 1:30:27 AM Eastern Standard Time,=20 marv@lancaironline.net writes: The equations don=E2=80=99t lie. =20 We did the numbers for the IO-720 that one of our friends tried ( rather unsuccessfully - - it went slower with the belt driven supercharger than it did without). =20 The equations showed why. The blower required a lot of horsepower. It wa= s not 70, but it was close. =20 Regards, George Gentlemen, =20 I have been following this friendly, yet heated, debate on the merits of=20 belt and turbine driven superchargers for the past few days. While I have fo= und=20 it interesting as well as humorous, I would like to ad my two bits to the=20 discussion. =20 First, the thermodynamic principles behind supercharging and engine power=20 output need to be understood. The fundamental advantage of supercharging is=20= that=20 it allows an engine of smaller displacement to develop the power of a larger= =20 model, by improving its volumetric efficiency. Obvious enough. =20 Unfortunately, you seldom get something for nothing, and the =E2=80=9Cmain= =E2=80=9D price=20 here is the power required to compress the intake air. Assuming the compres= sor=20 to be adiabatic (no heat loss), the power required is P =3D=20 [(p1*v1)/(k-1)]*[1-(p2/p1)^[(k-1)/k]*kg/m, where P =3D power, p=3Dpressure,=20= v =3Dspecific volume, and k=20 =3D the ratio of specific heats, or 1.4 for air near atmospheric conditions.= Of=20 these variables, we can obtain p1 and v1 directly from the air tables and p2= =20 is manifold pressure. Without an intercooler, the only thing left is to divi= de=20 by the efficiency of the supercharger. =20 Without an intercooler the power imparted to the pistons as a result of the=20 supercharger is roughly equivalent to the non supercharged power multiplied=20= by=20 v1/v2. v2 is given by v1*(p1/p2)^(1/k). =20 The discharge temperature of the compressor is given by T2=3DT1(p2/p1)^[(k-1)/k] =20 Assume you are flying at 18k, (50.5 kPa) with a supercharger that puts out=20 50.5 kPa, an engine that consumes 0.2 cubic meters of air per second (cms) a= nd=20 makes 300 hp at sea level manifold conditions. (I just invented the engine,=20= don=E2=80=99 t try to look it up) =20 v2 is 1.45 cum/kg * (50.5 kPa/101 kPa)^-1.4 =3D .884 cum/kg note: while MAP is equivalent to sea level, v2 is 8.3% higher due to=20 compression heating. In other words the manifold air is less dense. =20 Mass flow is 0.2 cms /.884 cum/kg =3D 0.226 kg/sec =20 P=3D[(50.5 kPa*1.45 cum/kg)/.4]*[1-(101/50.5)^(.4/1.4)]*.226 kg/sec=20 =3D 9061 watts or 12.15 hp. Assuming an efficiency of 80% results in about 15 hp to run the supercharger =20 The normally aspirated power at altitude is roughly sea level power=20 multiplied by the ratio of manifold specific volume: 300 hp * 0.816 / 1.45 =3D 169 hp =20 The supercharged power at the piston is 169 hp * 1.45/.884 =3D 277 hp =20 The net supercharged power is then 277 hp =E2=80=93 15 hp =3D 262 hp =20 So the net gain from the supercharger is 262-169 =3D 93 hp =20 George, am I missing anything here? =20 The compressor discharge temp is 252 K (101/50.5)^(.4/1.4) =3D 307 K or 34.2 C, or 93.5 F, however you like it. =20 At this point, I doubt if there is a great deal of difference between a=20 turbo, a belt or a gear. The added complexity of the turbo, including increa= sed=20 lubrication and cooling requirements, probably offsets much of the benefit o= f=20 using that waste energy from the exhaust. =20 Fly down low and things get a tad more interesting. If the engine was not=20 modified for the supercharger installation, then I can=E2=80=99t see how it=20= will be able=20 to utilize much boost without self destruction. The cylinder compression rat= io=20 just isn=E2=80=99t that far from the detonation limit when the factory sells= the=20 engine. Burning a higher octane fuel will allow a little more boost, but we= =E2=80=99re=20 still not looking at huge gains before detonation makes worm food out of the= =20 aircraft. If someone knows better, I would like to hear the explanation. Ric= k,=20 what MAP are you running around the pylons with your stock engine? =20 In a pylon race I would be surprised if there was a major difference between= =20 the turbine and the belt driven supercharger. The belt supercharger=20 installations I have seen (all cars) don=E2=80=99t have space for an interco= oler, which should=20 probably give the edge to the turbo in an engine modified for pressurized=20 induction. At low boost, the pressure drop across the intercooler, combined=20= with=20 the cooling drag might offset the density increase. =20 In an airplane used for typical GA flight, a turbocharged engine has to make= =20 the most sense. A wastegate is simply much more efficient than either a pop=20 off valve or a throttle. Yes, you could use a clutch on the belt or gear dri= ve=20 but you then are left with an all or nothing configuration and belts and gea= rs=20 use some power even when they are unloaded. Then again, as an afterthought /= =20 add-on feature the simplicity of a belt driven supercharger, combined with a= =20 lower price tag might make it the more attractive option. =20 I will grant that the above calculations are simplified, but they should be=20 in the ball park. Of course we still haven=E2=80=99t looked at the drag loss= es=20 associated with cooling the turbo, intercooler or the additional heat load f= rom the=20 engine. And then there is the additional mass of the supercharger installati= on. =20 It has been suggested that belt driven superchargers are foolish because a=20 calculation of a certain supercharger on a certain engine in a certain aircr= aft=20 showed that it would be slower with than without. Perhaps a certain=20 combination of components will be slower at low altitude. This does not make= the concept=20 of the mechanically driven supercharger fundamentally flawed. It simply show= s=20 the importance of properly sizing the components. Remember that the P38 used= =20 mechanically supercharged engines back in the 40=E2=80=99s. The first batch=20= sold to=20 England were delivered without the supercharger, as it was considered to be=20 sensitive technology in the day. The Britts considered these first planes to= be=20 totally useless. I think the capability of the mechanical supercharged model= s=20 speaks for itself. =20 It has also been suggested that racing to within 5 feet of first place is=20 proof that a belt driven supercharger is the best way to go. First, let me=20 commend Rick on his success on the course. I really respect anyone who refus= es to=20 follow the crowd, especially when they are competitive. However, there is a=20 whole lot more to racing than horsepower, and there is a lot in racing that=20= doesn=E2=80=99 t apply to everyday operation. =20 While there may be some magic in Rick=E2=80=99s supercharger, it is just as=20= likely=20 that his airplane is a little bit slicker or that he is a better pilot. Let= =E2=80=99s=20 face it, a 1% reduction in drag will buy just as much speed as a 1% increase= in=20 power. =20 That may have been a little more than two bits worth.=20 =20 Rob -------------------------------1111195125 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Content-Language: en
In a message dated 3/18/2005 1:30:27 AM Eastern Standard Time, marv@lan= caironline.net writes:
  The equations don=E2=80=99t lie.
&nb= sp;
  We did the numbers for the IO-720 that one of our friends tri= ed ( rather
unsuccessfully - - it went slower with the belt driven superc= harger than it
did without).
 
  The equations showed wh= y.  The blower required a lot of horsepower.  It was
not 70,&nb= sp; but it was close.
 
  Regards,  George

Gentlemen,

 

 I have b= een following this friendly, yet heated, debate on the merits of belt and tu= rbine driven superchargers for the past few days. While I have found it inte= resting as well as humorous, I would like to ad my two bits to the discussio= n.

 

First, the thermodynamic principles behind supercharging and=20= engine power output need to be understood. The fundamental advantage of supe= rcharging is that it allows an engine of smaller displacement to develop the= power of a larger model, by improving its volumetric efficiency. Obvious en= ough.

 

Unfortunately, you seldom get something for nothing, and the=20= =E2=80=9Cmain=E2=80=9D price he= re is the power required to compress the intake air.  Assuming the compressor to be adiabatic (no heat los= s), the power required is P =3D [(p1*v1)/(k-1)]*[1-(p2/p1)^[(k-1)/k]*kg/m, w= here P =3D power, p=3Dpressure, v =3Dspecific volume, and k =3D the ratio of= specific heats, or 1.4 for air near atmospheric conditions. Of these variab= les, we can obtain p1 and v1 directly from the air tables and p2 is manifold= pressure. Without an intercooler, the only thing left is to divide by the e= fficiency of the supercharger.

 

Without an intercooler the power imparted to the pistons as a= result of the supercharger is roughly equivalent to the non supercharged po= wer multiplied by v1/v2. v2 is given by v1*(p1/p2)^(1/k).

 

The discharge temperature of the compressor is given by

T2=3DT1(p2/p1)^[(k-1)/k]

 

Assume you are flying at 18k, (50.5 kPa) with a supercharger=20= that puts out 50.5 kPa, an engine that consumes 0.2 cubic meters of air per=20= second (cms) and makes 300 hp at sea level manifold conditions. (I just inve= nted the engine, don=E2=80=99t try to look it up)

 

v2 is 1.45 cum/kg * (50.5 kPa/101 kPa)^-1= .4 =3D .884 cum/kg

note: while MAP is equivalent to sea leve= l, v2 is 8.3% higher due to compression heating. In other words the manifold= air is less dense.

=  

Mass flow is 0.2 cms /.884 cum/kg =3D 0.2= 26 kg/sec

=  

P=3D[(50.5 kPa*1.45 cum/kg)/.4]*[1-(101/5= 0.5)^(.4/1.4)]*.226 kg/sec

=3D 9061 watts or 12.15 hp.

Assuming an efficiency of 80% results in=20= about 15 hp to run the supercharger

=  

The normally aspirated power at altitude=20= is roughly sea level power multiplied by the ratio of manifold specific volu= me:

300 hp * 0.816 / 1.45 =3D 169 hp

=  

The supercharged power at the piston is 1= 69 hp * 1.45/.884 =3D 277 hp

 

The net supercharged power is then 277 hp= =E2=80=93 15 hp =3D 262 hp

=  

So the net gain from the supercharger is=20= 262-169 =3D 93 hp

=  

George, am I missing anything here?

=  

The compressor discharge temp is 252 K (1= 01/50.5)^(.4/1.4) =3D 307 K

or 34.2 C, or 93.5 F, however you like it= .

 

At this point, I doubt if there is a great deal of difference= between a turbo, a belt or a gear. The added complexity of the turbo, inclu= ding increased lubrication and cooling requirements, probably offsets much o= f the benefit of using that waste e= nergy from the exhaust.

 

Fly down low and things get a tad more interesting. If the en= gine was not modified for the supercharger installation, then I can=E2=80= =99t see how it will be able to utilize much boost without self destruction.= The cylinder compression ratio just isn=E2=80=99t that far from the detonat= ion limit when the factory sells the engine. Burning a higher octane fuel wi= ll allow a little more boost, but we=E2=80=99re still not looking at huge ga= ins before detonation makes worm food out of the aircraft. If someone knows=20= better, I would like to hear the explanation. Rick, what MAP are you running= around the pylons with your stock engine?

 

In a pylon race I would be surprised if there was a major dif= ference between the turbine and the belt driven supercharger. The belt super= charger installations I have seen (all cars) don=E2=80=99t have space for an= intercooler, which should probably give the edge to the turbo in an engine=20= modified for pressurized induction. At low boost, the pressure drop across t= he intercooler, combined with the cooling drag might offset the density incr= ease.

 

In an airplane used for typical GA flight, a turbocharged eng= ine has to make the most sense. A wastegate is simply much more efficient th= an either a pop off valve or a throttle. Yes, you could use a clutch on the=20= belt or gear drive but you then are left with an all or nothing configuratio= n and belts and gears use some power even when they are unloaded. Then again= , as an afterthought / add-on feature the simplicity of a belt driven superc= harger, combined with a lower price tag might make it the more attractive op= tion.

 

I will grant that the above calculations are simplified, but=20= they should be in the ball park. Of course we still haven=E2=80=99t looked a= t the drag losses associated with cooling the turbo, intercooler or the addi= tional heat load from the engine. And then there is the additional mass of t= he supercharger installation.

 

It has been suggested that belt driven superchargers are fool= ish because a calculation of a certain supercharger on a certain engine in a= certain aircraft showed that it would be slower with than without. Perhaps=20= a certain combination of components will be slower at low altitude. This doe= s not make the concept of the mechanically driven supercharger fundamentally= flawed. It simply shows the importance of properly sizing the components. R= emember that the P38 used mechanically supercharged engines back in the 40= =E2=80=99s. The first batch sold to England were delivered without the supercharger, as=20= it was considered to be sensitive technology in the day. The Britts consider= ed these first planes to be totally useless. I think the capability of the m= echanical supercharged models speaks for itself.

 

It has also been suggested that racing to within 5 feet of fi= rst place is proof that a belt driven supercharger is the best way to go. Fi= rst, let me commend Rick on his success on the course. I really respect anyo= ne who refuses to follow the crowd, especially when they are competitive. Ho= wever, there is a whole lot more to racing than horsepower, and there is a l= ot in racing that doesn=E2=80=99t apply to everyday operation.

 

While there may be some magic in Rick=E2=80=99s supercharger,= it is just as likely that his airplane is a little bit slicker or that he i= s a better pilot. Let=E2=80=99s face it, a 1% reduction in drag will buy jus= t as much speed as a 1% increase in power.

 

That may have been a little more than two bits worth. =

 

Rob

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