X-Virus-Scanned: clean according to Sophos on Logan.com Return-Path: Sender: To: lml@lancaironline.net Date: Tue, 28 Dec 2010 21:51:56 -0500 Message-ID: X-Original-Return-Path: Received: from web81202.mail.mud.yahoo.com ([68.142.199.106] verified) by logan.com (CommuniGate Pro SMTP 5.3.11) with SMTP id 4656565 for lml@lancaironline.net; Tue, 28 Dec 2010 09:35:20 -0500 Received-SPF: none receiver=logan.com; client-ip=68.142.199.106; envelope-from=cwfmd@yahoo.com Received: (qmail 23316 invoked by uid 60001); 28 Dec 2010 14:34:46 -0000 DomainKey-Signature:a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com; h=Message-ID:X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type; b=qwNL1xxydkOYGl8Thi5uJlZCkmnDBg5Fqe6YovsBomAl3VVtIZzFOOJ3mDbWLAmzfkOeSk6LQ6xBGHaai1SEyQ1XtBlhOYgeZC7kmQ4rM4Q4zcc/9hl+dD0VS7micwnk3KH8M38ngag09TXe86MQtNwadzP21Wdunv48LbzWEwU=; X-Original-Message-ID: <71788.22830.qm@web81202.mail.mud.yahoo.com> X-YMail-OSG: NaFIWBsVM1mfCQVpTe.FOK.lBxk9yyu2WsSvvdIVru89PlP We7MoCVHbz258Xh3j5g9E1TK0dx0qA7xDBE73yBdxaaZLfnyPB2RVEgAU_SZ oPtSE6FnrDVndOEXTOhE5f7FL9TU5ciH1iOc6gP.Mkrst31YILSU8LGlx.IV .rX1pWVP0tEfU97aNuZPcz87JCzVKutZb7ttD4av1QW6Zd2fABoBvyo431I6 yrWEXuNQZJ2mZrYTvHYcrWYqDJVaKtZLBMcGFGrLUyaFixX9s7BUexHgviUr S.zN99fNz6z_5nMH_H4h3M4Pzr5E698a.Gy12UrXKupVClgb09gZhn0Ol2lj jID1H33RfhvCgX89lAqQhpp2DJLMut6j.kEf9MgelMTz.5Z4sxwIgcb7Tzqy GSv5.Z7fOsCDW Received: from [76.30.87.99] by web81202.mail.mud.yahoo.com via HTTP; Tue, 28 Dec 2010 06:34:45 PST X-Mailer: YahooMailClassic/11.4.20 YahooMailWebService/0.8.107.285259 X-Original-Date: Tue, 28 Dec 2010 06:34:45 -0800 (PST) From: William Miller Subject: Re: googlePerf or "cubic gets big", buy less S, not FF X-Original-To: lml@lancaironline.net MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="0-624998535-1293546885=:22830" --0-624998535-1293546885=:22830 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Marv, If it is not too late, I would like to withdraw and revise this post. Upon = review, there is an error in the analysis of V, as IAS vice TAS. Interestin= gly, the density correction for altitude only appears to the first power, r= ather than the 3rd as I represented here. Thanks Bill Miller --- On Mon, 12/27/10, William Miller wrote: From: William Miller Subject: googlePerf or "cubic gets big", buy less S, not FF To: lml@lancaironline.net Date: Monday, December 27, 2010, 10:53 AM Following up on the perf comparison idea, here's a handy tool, discovered o= n Google Calculator, for all of us who prefer not to drag out the Mathemati= ca or Matlab, just to do unit conversion. Based on the power formula and co= nservation of Energy(rate) the formula for level steady state cruise perf i= s: F=3D1/2 rho V^2 S =A0=A0 and=A0=A0=A0=A0 Power=3DF*V =3DHP =A0=A0=A0 1/2 rho V^3 S =3D HP =3D Fuel Flow(FF) * 13.7 HP/(gal/hr)=20 =A0thanks Jeff for the conversion factor. LOP <65% Substitute this mess into Google calculator, just like a search I backed out S for N330FF to .3185m^2, unfortunately S will vary with Gross= weight, because it incorporates induced drag =A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=0A S=A0=A0=A0=A0=A0=A0= =A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 V=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0= =A0 rho=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0= =A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 FF input =3D> 0.3185m^2*((187 kts)^3* 1.225 kg m^-3/(2))=A0 /(17gal/hr*13.7hp/= (gal/hr) =A0(0.3185 (m^2) * ((((187 kts)^3) * (1.22500 (kg (m^(-3))))) / 2)) / (((17= (gal / hr)) * (13.7 hp)) / (gal / hr)) =3D 1.0000512 ignore the round off error, this is back of the napkin okay? input =3D>m^2*(( kts)^3* 1.225 kg m^-3/(2))=A0 /(gal/hr*13.7hp/(gal/hr) =A0((m^2) * (((kts^3) * (1.22500 (kg (m^(-3))))) / 2)) / (((gal / hr) * (13= .7 hp)) / (gal / hr)) =3D 8.16275764 =D7 10-6lets call 8.1627e-6 the dimens= ionless conversion factor =A0S V^3 =3D8.1627e-6 FF=A0 with dimensions=A0 S[m^2]=A0 V [kts IAS]=A0 FF(= galUS/hr) now you can relate any two input variables to the third And also remind us why there is no free lunch, becuz =A0 =A0 =A0 =A0 =A0 = =A0 FF : V^3 Disclaimer: yes IAS not=3D CAS EAS etc. This is a linear formula and everyb= ody knows the drag curve is not a straight line.... there are many improvem= ents ahead, but this is fun for front side, steady state, cruise=0A perf. H= ow much did you lower your S by replacing that P-51 scoop with a NACA intak= e? One last math trick: Divide the junk behind the decimal point by 3 to get t= he approximate cube root. How much more power required to go 10% faster?=A0= 1.1^3 =3D 1.331 or 33.1% more pwr. =0A=0A=0A=0A=0A=0A=0A=0A =0A=0A=0A --0-624998535-1293546885=:22830 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
Marv,
If it is not too late, I would like = to withdraw and revise this post. Upon review, there is an error in the ana= lysis of V, as IAS vice TAS. Interestingly, the density correction for alti= tude only appears to the first power, rather than the 3rd as I represented = here.
Thanks
Bill Miller

--- On Mon, 12/27/10, William Mill= er <cwfmd@yahoo.com> wrote:
From: William Miller <cwfmd@yahoo.com>
Subject: googlePerf or "c= ubic gets big", buy less S, not FF
To: lml@lancaironline.net
Date: Mo= nday, December 27, 2010, 10:53 AM

Following up on the perf comparison idea, here's= a handy tool, discovered on Google Calculator, for all of us who prefer not to drag out = the Mathematica or Matlab, just to do unit conversion. Based on the power f= ormula and conservation of Energy(rate) the formula for level steady state = cruise perf is:
F=3D1/2 rho V^2 S    and   &nbs= p; Power=3DF*V =3DHP
    1/2 rho V^3 S =3D HP =3D Fuel Fl= ow(FF) * 13.7 HP/(gal/hr)
 thanks Jeff for the conversion factor. = LOP <65%

Substitute this mess into Google calculator, just like a= search
I backed out S for N330FF to .3185m^2, unfortunately S will vary= with Gross weight, because it incorporates induced drag
  &nb= sp;            =   =0A S         &nbs= p;       V      = ;          rho  &nbs= p;            &= nbsp;           &nbs= p;       FF
input =3D> 0.3185m^2*((187 = kts)^3* 1.225 kg m^-3/(2))  /(17gal/hr*13.7hp/(gal/hr)

 

= (0.3185 (m^2) * ((((187 kts)^3) * (1.22500 (kg (m^(-3))))) / 2)) / (((17 (g= al / hr)) * (13.7 hp)) / (gal / hr)) =3D 1.0000512

ignore the round off error, this is back of the napkin okay?<= br>

input =3D>m^2*(( kts)^3* 1.225 kg m^-3/(2))  /(gal/hr*13.7hp/(ga= l/hr)

((m^2) * (((kts^3) * (1.22500 (kg (m^(-3))))) / 2)) / (((gal= / hr) * (13.7 hp)) / (gal / hr)) =3D 8.16275764 =D7 10-6

 
lets call 8.1627e-6 the dimensionless conversio= n factor
 S V^3 =3D8.1627e-6 FF  with dimensions  S[m^2]&= nbsp; V [kts IAS]  FF(galUS/hr)
now you can relate any two input va= riables to the third
And also remind us why there is no free lunch, becu= z             FF : V^3

Disclaimer: yes= IAS not=3D CAS EAS etc. This is a linear formula and everybody knows the d= rag curve is not a straight line.... there are many improvements ahead, but this is fun for f= ront side, steady state, cruise=0A perf. How much did you lower your S by r= eplacing that P-51 scoop with a NACA intake?

One last math trick: Di= vide the junk behind the decimal point by 3 to get the approximate cube roo= t. How much more power required to go 10% faster?  1.1^3 =3D 1.331 or = 33.1% more pwr.


=0A=0A=0A=0A=0A=0A=0A= =0A

=0A=0A --0-624998535-1293546885=:22830--