Warner, Edward P

English

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TECErJ IC1>.L NOTES 
rAT IONAL. DVISORY COMMITTEE FOR AERONAUTICS. 
No. 215 
THE CALCULATION OF WING FLOAT DISPLACEMENT 
IN SI TG E-FLOAT SEAPLANES. 
By Edward P. ~arner, 
~tassachusetts Insti tute of Technology. 
March , 1925. 
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NATIOIAL ADVISOR! OO}.1HITTEE FOR AEROTAUTICS. 
TEC':1NICAL TOTE NO. 215. 
THE CALOULATION OF WING FLOAT DISPLACEMENT 
IN SI1JGLE-Fl·OAT SEAPLAlJES . 
By Edward P. '1arner. 
The lateral stabili ty of all single-float seaplanes and 
flying boats except those of the Dornier type with lateral ex-
tensions on the hull itself must be assured by the use of auxil-
iary floats at the wing tips ~ these floats being mounted high 
enough so that they make contact wi th t he water only when the 
seaplane is heeled over to one side or the other and so that on-
ly one of the wing floats can be in contact with the water at a 
giv en time. 
In calculating the proper size for such wing floats, the 
stability of the main central float is often entirely neglected, 
the position of center of buoyancy being assumed independent of 
the angle of inclination. The weight carried by one of the aux-
iliary floats in still ~ater and still air can then be calcu-
lated directly by takin moments around the center of buoyancy 
with the nachine in the inclined position, and the total volume 
which the wing floats should have can be calculated if it is as-
sumed that a fixed reserve of buoyancy is desirable there, just 
as it is for the main float. It is then necessary only to mul-
tiply the we i ght carried by the wing float under ideal conditions 
,J 
" 
[.A~C .A. Technical Note No . 215 2 
by a fixed constant to find the desirable total displacement. 
The application of this me thod has been explained in detail with 
calculations for a number of specific examples, in a recent pub-
lication.(Rcference 1). 
The use of a fixed reserve of buoyancy has several possible 
disadvantages in certain s~ecial cases. In the first place, it 
is liable to lead to incorrect results for machines with a very 
low center of gravity, such as flying flonts. The instability 
of the main float a lone is small in such cases, and even a 100 
percent reserve may represent a very small absolute addition to 
the size of the wing float . It will be observed that the re-
se rve buoyancy of the wing floats is exceptionally large on most 
flying boats which have proven satisfactory in actual service. 
On the NC , for example, the reserve was 490 percent. A method 
which would give a con8t~nt independent of size and height of 
c . g . would obviously be desirable. Second, and by similar rea-
soning, the use of a constant reserve of buoyancy takes no ac-
count of the stability of the main float. It is conceivable 
that two different floats might be designed for a given machine, 
and that the ne gative lateral mctacentric height with one of 
them would be 3 feet, while with the other it would be only 3 
inches. Obviously, if t he central float itself has a consider-
abl e measure of stability the size of the wing floats can be re-
duced. Third, the method involving a constant reserve of buoy-
ancy cannot be applied at all in those cases where there is a 
T.A.C.A. Tech~ical No te rO . 315 3 
small positive metacentric height. A hull of the Dornier type, 
for example, might b e so desi gned "as to locate the metacenter a 
few inches above the c. g . There would then be no weight car-
ried on the wing float when the seaplane was at rest under ideal 
conditions, as the machine would float on an even keel, but, 
nevertheless, wing floats would actually be required under serv-
ice conditions to provide a sufficiently large reserve of sta-
bility. 
In seeking another me t hod it seems lo gical to turn directly 
to the concept of metaeentric height, always used in investi-
gating the stability of a single floating object. ¥~en it is 
said that a twin float seaplane has a lateral metacentric heig~t 
of 12 feet the implicQtion is that t he oenter of gravity could 
be raised 12 feet from its actual position before the machine 
would become laterally unstable in still water a nd would fail to 
return to its original position of equilibrium if sli ghtly dis-
turbed therefrom. A fictitious raising of the center of gravity 
may be used in an analo gous manner in determining the size of the 
wing float. Instead of stating that such a float must have 100% 
reserve of buoyancy, it may be specified simply that the float 
must be large enough so that it would hold the wing out of water 
if the center of gravity were raised x feet from its present 
position, and that procedure overcomes all of the principal ob-
jections just stated against the other method. 
Obviously, the height by which it should be possible to 
• 
l ·A·C.A. Technical Note No~ 215 4 
raise the center of gravity should bear some definite relation to 
the desirable metacent ric height of a twin-float system. Diehl 
has shown (Reference 1) that present practice endorses the use 
of twin-floats so set that thc transverse metacontric height is 
equal to 13 + . 002 W, where W is the total weight of the air-
plane in pounds . Manifestly, however, it would be unnecessary 
to allow for raising the c.g . by that full amount whcn auxiliary 
floats are employed, as the auxiliary floats are normally out of 
the water and the inclining moments when running through waves 
are therefore much less than those arising vlhen there are two 
main floats of equal size continually carrying the seaplane. 
Comparison of the characteristics for existing seanlanes, simi-
lar to the compari son made by Diehl in deriving his constants, 
suggests that on the average the center of gravity should be 
assumed raised by about one-half of the desirable metacentric 
height as givcn by Diehl's formula, but that the exact ratio 
should be a funct ion of the angle of inclination to submerge the 
wing float completely and that it should vary lineally from a 
value of .8 at 30 inclination down to one of .2 at 12 0 , remain-
ing constant for angles of inclination higher than that. Fig . 1 
shows the nature of the variation. 
N. A. C. A. Techni c[l,l No to No . 2i5 5 
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Fig. 1 
The formula for the displacement of each wing float then 
becomes: 
~vr = W[GM + k (13 + .002 W)Jtan¢ 
s 
where ~ is t h e total buoyancy of a wing float, Vi the wei ght 
of the seaplane, GM its negative metacentric hei ght, k the 
coefficient plotted in Fig . 1, :l> the angle of tilt to submerge 
a wing float, and s the distance from each wing float to the 
plane of symmetry of the seaplane . 
Reference 
1. W. S. Diehl: Static Stabi li ty of Seaplane Floats and Hulls. 
N.A.C .A. Techni cal Note No. 183. 1924. 


The calculation of wing float displacement in single-float seaplanes

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