This report presents a new theory which makes it possible to interpret the resistance and the trimming moment for any loading of a planing aircraft when these values are given for one load. This application of the new theory forms the basis of the present paper. Derivations of various conversion formulas are given as well as numerous examples

Schroder, P

English

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CASE 11 
T	 -, T. i.	 O_AJi 
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

No. 619 
DETERMINATION OP RESISTANCE AND TRIMMING MOMENT

OP PLANING WATER CRAFT 
By P. Schrer 
Zeitschrift fir Flugtechnik und Motorluftschif±'ahrt

November 28, 1930 
Ver1a von R. O1.enbourg, Milnchen und. Berlin 
FILE COpy IQbe returned to 
*N fl	 f t NatIon 
MvisQry Comrrittes 
for Aemnau

	
ashinton	 WUh(ngtn, 0. C, 
M ay , 1931
https://ntrs.nasa.gov/search.jsp?R=19930094797 2020-06-17T00:28:38+00:00Z
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
TECHNICAL MEMORANDUM NO. 619 
DETERMINATION OP RESISTANCE AND TRIMMING MOMENT

OP PLANING WATER CRAFT* 
By P. Schr8der 
I. Theory 
Notation 
W = resistance 
.	 ...	 •.	 of water craft at
M = trimming moment 
•1	 j planing speed. v.

A = lift 
=
	
	 = lift-drag ratio.
A 
=	 = trimming moment with respect to lift. 
In conformity with previous reports*, C = constant and. 
constant when	 = constant. 
Thus it becomes possible to interpret the resistance and. 
the trimming moment for any loading of a planing aircraft wnen 
these values are givefi for one load. This applicätionof the 
new theory forms the basis of the present paper. 
den Wasserfahrzeugen,' Zeitschrift fur Plugtechnik und. Motorluft-
schiffahrt, Vol. 21, No. 22, November 28, 1930. 
**p, Schrod.e •".Take-ff of Seapianes Base.on	 Nw..Theory of 
Reduction in Hydrodynamics, t1 Zeitschr±ft fur Fugtechnik und Mo-
tor1uftschifht, January 14, 19 3 1 (to be issixed. apN.A.C.A. 
Technical Memorandum No. 621). 
P. chrr8der-, "AReduction Theory for Planing Water .Aircraft and. 
I.ts. Exp erimental Verificat.on," Ber.icht der. hamburischen Schiff -
bauversuchsa.nstalt, July 14, 1930.. 	 .	
.	 :	 ..	 : 
.	
.
2	 . N.A.'C.	 .Tøchnica1'MenorandumTo. 619 
	
Derivatiii.o' 'Varo	 C,pnyer SI on. Formulas 
:Cse. l.'.ø .. 'diffQre. nt loads of hyd.rovanes 
	
Given:	 and. .'.M	 for a. l,oad A1 ' = constant; 
Find:	 W2 and. M2 ' for ar lpd.:A = constant. 
The equation defining the corresponding peed.s now becomes: 
	
:V 2	 .;.	 (1) 
A1 
or	
= ' 1 	 (2) 
	
By virtue of,	 cA. and. M	 P0 A, these speeds are 
M 
a. 
	
1	 2	 .	 '.	 1	 2 
and. W2 and	 2 are now expressed. as..... 
A2 
W1	
' :'	 .	 (3) 
and	
'	 1 
A
	
•	 ...
	 (4) 
These three equations (2), (3), and. (4)', now assume a general 
signlfiáance, iñsmuchas they retain their 'validity' even' .hen 
A 1 and- A 2 are arbitiary speed- functions. 
Case . 2 - Conversion of' resistance 
and trimxrin moment curves of e hydrov2ne 
'for,app lication.as se.aDlane floa.t . 	 ' •. .. 
	
Given	 W1 aid W 1 for a load A 1	 constant 
	
Find.	 W2 and- M 2 for a load A2 = A (v). 
Thi:cas .f A, be,in.g'a p,rescri.bed.functionof.thé speed is 
always applicable when the pertinent vane is to be used as sea-
plane float. I-f A 1 is tile roas wei'ght .o the. air.c,raft, the 
load formula by fixed- trim is:
N.A.C.A. Technical Memorandum No. 619 	 3 
V22\ 
	
A 2 = A 1
 1 - ---)	 (5) 
where v = getaway speed. Now we write the quotient ' A2 /A 1
 in 
(2), resolve it according to v 2 , and obtain the relation for 
computing the corresponding speeds
vi 
=	
•(6) 
/1+()2 
Then we insert the quotient A 2/A 1 .  of (5) in (3) and. (4), and 
use (6) for elimine.ting v 2 which yield the formulas for 
and M2 as
W2	 ----	 (7) 
1 + (!-
vsj
	
2	 (8) 
'V 
Case	 3 
Given:	 and M 1 for a load. A 1	 A (v), 
Find:	 W2 and. M2 for a load A2 = A2
 (). 
This case has practical significance when resistance and. 
moment of a seaplane flotation gear have been measured for a 
certain wing and. it is subsequently. desired to apply these val-
ues to some other gross weight and other wing. In addition, it 
contains the possibility of embo4ying the effect of the wind. in 
take-off investigations of seaplanes. 
o) Conversion of the take-off resistance curves and. trim-
ming moment curves of a seaplane flotation gear to different 
wings and gross weights: 
e assume	 and. M 1 measured for 
/	 v 2\ 
A1 = G 1 l -
	
( 9) 
1 
where G 1	 gross weight of aircraft upon which the measurement 
was based., and. v 51 = relevant getaway speed. The new gross
4	 N.A.C.A. Technical Methorandum No. 619 
weight is to be	 G-,	 and the getaway sp e&d. with the new wing is 
to be
	 v 52 .	 Then the loading
V2\. 
A2	 G2 (1 -	 is requested (10) 
Vs2 
A calculation analogical to the preceding case yields with abbre-
viation
N2	 =	 1 - (I1_)	
+ 
(ri-) (ii) 
the following reu1ts:
V2	 =	 V 1	 N	 ; (12) 
=	 W1 N 2 (13) 
M2	 =	 M 1
 N 2 (14) 
)	 Effect	 of wind in t.àke-ff	 studies of	 seaplanes: 
Assume as measured,	 W1	 and M1	 for take-off with zero wind 
by lift
G(l. (15) 
where	 G = gioss weight and	 v 5 = getaway speed in zero wind, 7 2 an4 M 2 are	 to . becorputed foW	 ru/s head wind, Because of 
the greater unloading•by the wings the loading of the flOtation 
gear	 remains	 as	 .• 
.:[ v+w2 
A 2	 G - (a__ , (16) 
L1 
The calculation of	 v2	 reveals 
(V2 (fl21 V2 =	 w + v	 1 - (_[l - 
v5)	 \VsJ (17) L J 
and the elimination of 	 V2	 sets forth the quotient A2 /A 1	 as: 
=	
+	
__ !
[	
-
(18)
N.A.C.A. Technical Memorandum No. .619
	 5 
which, substituted in (3) and (4), supplies the desired values 
for W2
 and 1V12.
Graphic Method 
The preceding analytical problems can equally be solved by 
graphical means. Given curve
	 or M1
 under 'the secondary 
assumption that A.1	 A1. (v) , find	 or M 2 , respectively, 
for the assumption A 2	 A2 (v). Equations (2.), (3), and (4) 
may be written as 
•	 .:	 .	 Ma	 A2	 - 
Wi	
-, A 1
 - 
on which the following method can be based: 
Plot A 1
 and A 2 , as well as. W 1 and M 1
 over. v 2 . For the 
arbitrarily chosen speed v 1 on the W1
 , M 3. , and A 1 curves, 
we have point P 1 , which we connect with •the origin of the co-
ordinates 0. The connecting' S
 line 'intersects the prescribed 
lift A 2
 in point	 2• The ratio of the distances OP2 to OP1 
is' the same.. in..all..three	 Lagrams, namely, 'T/v 2 , M/2, and A/v?, 
thus revealing P2
 as the point of the desired resistance and 
moment curve. This representation yields W2
 and M2
 in simple 
fashion for any stage of the prescribed lift. 
II. Examples of Application 
The examples: have, been selected: so:. as
	 allow, the' om 'äri-

son of the mathematical. figures with the test'.data. This applies 
to all'but the 1astexamp1e where the lack of suitable data maks 
this impossible.	 . . .''	 .	 .	 . .	 '.	 . . 
The solutions are given in graphical form. The points de-
fined by.calculition and graphic. cc tuction'respect.iély,. are 
indicated by small circles in the first four examples. The per-
tinent curve in question was in&luded for comparison inconformity 
with measurements made prior.to the development of the conver-. 
sion method 6	 .	 . 
1 l Example - donversion of the resistance of a Jydrovane 
Given resistance curve W1
 (Fig 0
 1) of a 1 : 8 scale 
model of a flat-bottOm hydrovane (designed by Engineer 
Ellinghausen,	 emen), pertaining to loading 
A 1	 6,5 tons;
6	 N.A.C.A. Technical Memorandum No. 619 
Find, the resistance curve W2
 for loading A 2
 = 5.5 
tons. The lines emanating from origin 0 defin the 
corresponding speeds. Each intersection point P1 
of such a line with curve W1
 has a relevant point 
P 2 on curve W2 , so that 
OP : OP1 = 5,5 : 6,5 = 0.847. 
This'-d.efi.nes W2 . The portion of..the W 2
 curve 'rom:2.5 to 4.5 
rn/s was measured. diiect.(Tet No 2681 of the Hamburg seaplane. 
channel 1aboatOry,. January, l28).
	 . . ..'	 ... 
2. Example - Compute the resistan.ce curve of twin floats: 
	
Given resistance curve W ]	 (Pig. 3) of a 1 : 6 scale 
model of twin floats for a seaplane with constant 
loading	 A.1	 2920 kg	 .:	 .	 .•	 . . . 
Find the resistance curve for loading 
A 2.	
.	 l	 1	 .	 .. 
with )00 km/h ,etaway speed. For the model we obtain 
A 1 = 2920	 6	 l352 kg 
	
=	 = 11.34 rn/s 
Figure 2 exhibits the construction of the.lift ratio A2/A1. 
The formula .
 OP. 2	 A2 : •A	 reveals a.point ;P2::,,Of the de-
sired .resistane curve on each line emanating from 0.: The 
plott.e. curve ,W2:,.was measured direct. (Re .por.t Jf 39/2 of the. 
D.V.L. (Deutsche Versuchsanstalt fur Luftfahrt), anuary 21, 1929, 
page 39). 
3..:Ex.rnple- CQm.pite .. the trim.niing .moiien.t.of twinHfloets:.. 
.•.Giv.en trimming :mQ.meflt curve	 (Fig. . 5) .
 of a .1 ::
	 . 
.. sca1emd.e1 of the twi:n:floats for a s.eaplane.with 
constant loading A 1 = 2400 kg; 
Pindthe .mome
.n:t. curve for the;same:tim f..or. 1o:ading: A2 
of the floats
•v2 
A2	 A1 (.1 -...---	 .. v5.!
N.A.C.A. Technical Memorandum No. 619 	 7 
for a seaplane with 84 km/h getaway speed.
	 e find: 
A 1 = 2400 : 6	 11.12 kg, 
84 
vs =
	
	
= 9.53 rn/s 
.).o 
,J 0 
Figure 4 represents the lift atio A 2 /A 1 . The points P 
which in the mmnt:diagram (Fig.5) ireveal the desIred moment 
M 2 , are defined by
OP2 : OP1	 A2 :. A1. 
The M 2 curve Was measured direct. (Report Jf 63/1 of the D.V.L., 
June 1?, 1929, pages 38 and 39 for 5 trim run). 
4. Example - Conversion of resistance curve of an aircraft

to a different gross weight: 
Given resistance curve W1
 of al: 6 scale model of 
twin floats for a prescribed loading 
A 1 = 
The gross weight is G' = 2400 kg and the getaway 
speed is 84 km/h, so that, as in the preceding exam-
ple, G1 = 11.12 kg, and v 5 = 9,53 rn/s. 
Find, the resistance curve for the same twin floats with 
a smaller wing and a lower gross weight, that is, 
G 2 ' = 0,75 G 1 ' = 1800 kg 
by identical wing loading, 
The latter implies that v 5 does not change. The new lift 
is
/ 
A 2
 = G2 l - 
where G	 1800 : 6 = 8.34 kg, as illustrated in Figure 6 for 
A 2 /A 1 . The srnall circles on curve	 2 of Figure 7 again con-
form to the condition
OP2 : OP1 = A2 : A1. 
The part curves shown are from direct measurements (Report 31
8	 .A.C.A, Technical Memorand.urnNo. 619 
63/1 of the D.1T.LS, June 12, 1929, page 36, and. Report Jf 63/1 
of the D . V,L,, Jine 14, 1929, page 30, 5 trim run). 
5. Example -. Inc1id.ing the effect of the wind, in take-off 
studies of se'aplanes: 
iven resistance curve W 1
 (Fig. 9) of twin floats for 
take-off with no wind.; 
Find. therefrom the resistance curve for take-off at

5 m/s, and w3	 10 rn/s head. wind.. 
Figure 8 contain the prescribed loading A 1 for w1
 = 0 
and the constructio.n of the lift ratios A s /A and A3 /A 1 . Fig-
ure 9 reveals the desired. resistance W2 and	 • The twin floats 
selected. produc. unfavorable resistances at high speeds, and the 
lowered. recistanco, owing to the wind, is Particularly notice-
able. 
Translation by J. Vanier, 
'Tational Advisory Cornitteo 
for Aeronautics,
2.0 
1.5
V1, kg

1.0 
.5 
1 
1 
A, kg
N.A.C.A. Technical Memorandum No. 619
	 Figs. 1,2 
012	 3	 4	 5	 6	 7 
v, rn/sec. 
Fig. 1 
012345 6 7
	 8	 9	 10 
v, ill/sec. 
Fig. 2'
3 
2 
W,kg
1 
10 
A,kg
5 
N.A.O.A. Technical Memorandum No. 619
	 Figs.3,4,5 
0123 4	 5	 6	 7	 8	 9 
v, rn/sec. 
Fig. 3
	
p	 A 
012345 6 7
	 8	 9	 10
v, rn/sec. 
1.5 
N, mkg 
1.0 
2.0 
2.5 
.5 
0
Fig. 5
v, rn/sec.
10 
A, kg
5 
2.0 
1.5 
1.0 
kg 
.5 
N.A.O.A. Technical Memorandum No. 619 	 Figs. 6,7 
0123 4 5 6 7
	 8	 9	 10 
v, rn/sec. 
Fig. 6 
012	 3.4	 5	 6	 .	 7 
v, rn/sec. 
IFig. 7
'1.I.i 
2000 
A,. kg 
1000
300 
W, kg 
200 
100
N.A.O.A. Technical Memorandum io. 619 	 Figs. 8,9 
103050	 70	 90	 110 
0 2040 60
	 80	 100
v, km/h 
Fig. 8 
500 I 
10 30
	 50	 70	 90	 110 
0 20 40	 60	 80	 100 108 
v, kin/h 
Pig. 9


Determination of resistance and trimming moment of planing water craft

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