FOREST AND STHEAM. 
3. For bai's of square section, giving the sa'rae ultimate 
Btrengtii of Cotapressiou, the alumiuuru bar gives 1.33 times 
the ultimate tesistalice to taendiug, and 2 03 times the elastic 
resistance to bending, is about of equai stiffness, and vs^eighs 
about 0.59 as much as the .steel bar. 
4. For bars of square section, giving the same elastic 
strength of compression, the aluminum bar gives 0.7 the 
ultimate resistance to bending and 1,07 times the elastic re- 
sistance to bending, is but 0.44 as stiff and weighs about 0.38 
as much as the steel bar 
5. For bars of square section of the same weight the alu- 
minum bar, giving 2 times the ultimate resistance to ten- 
sion, 2.8 times the elastic resistance to tension, 1.7 times the 
ultimate resistance to compression, 3.6 times the ela.stic re- 
This advantage of greatel' resistance to bending and gjteatei' 
stiffness, thus pronounced for square sections, is enormotisly 
greater for plating. With the saine weight, the aluminuiti 
plate oflfers over five times the ultimate resistance to bend- 
ing, nearly eight times tlie elastic resistance to bending, and 
is nine times as stiff. 
These remarkable results flow from the great moment of 
inertia in the case of aluminum sections, the metal added to 
supply the increase of area of cross section acting with large 
leverage about the neutral axis. The aluminum plate being 
three times as thick, the moment of inertia is twenty-seven 
times as great. This enormous increase in stiffness, as will 
be seen below, is of great advantage in the case of thin plates, 
which are necessarily deficient in stiffness. 
PIG. 15. 
Extiuction of Dynamic Forces. Work Done Within Elastic Limit. 
sistanre to compression, 1.875 times the ultimate resistance 
to shear, gives in addition 2.94 times the ultimate resistance 
to bending, 4 5 times the elastic resistance to bending, and 3 
times the stiffness. 
6. For plates of rectangular sections of the same width, 
giving the same ultimate strength of tension, the aluminum 
plate, of half tlie weight, gives 1 2fi times the ultimate re- 
sistance to bending, 1 94 times the elastic resistance to bend- 
ing, and 1.125 times the stiffness. 
7. For plates of rectangular section of the same width, 
giving the same elastic strength of tension, the aluminum 
plate, of about one-third the weight, gives 0.65 the ultimate 
resistance to bending, 0 99 the elastic resistance to bending, 
and 0.41 the stiffness. 
8. For plates of rectangular section of the same width, 
having the same weight, the aluminum plate, giving twice 
the ultimate resistance to tension, 2.8 times the elastic resist- 
ance to tension, gives in addition 5.1 times the ultimate re- 
sistance to bending, 7 S times the elastic resistance to bend- 
ing, and 9 times the stiffness. 
9. For I beams of the same weight and proportioned sec- 
tions, the aluminum beam gives 2.83 times the_ ultimate 
resistance to bending, 4 45 times the elastic resistance to 
bending, and 3,1 times the stiffness. 
10. For angle bars of the same weight and proportioned 
sections the aluminum angle gives 2.35 times the ultimate 
resistance to bending, 3 59 times the elastic resistance to 
bending, and 2 3 times the stiffness. 
11. For I beams of proportioned sections, giving the same 
ultimate resistance to bending, the aluminum beam has 1 39 
When resistance to bending and stiffness are themselves 
the objects of design, determining a form of section of large 
moment of inertia with the usual shapes, such, for instance, 
as I beams and angle bars, the advantages offered by alumi- 
num are more pronounced than in the cases of simple resist- 
ance. With equal weight,. it may be said broadly that the 
aluminum beam gives two and a half times the ultimate 
resistance, and is two and a half times as stiff. The effect of 
aluminum's high fraction of elasticity is again striking; 
when compared for elastic resistance, the aluminum beam 
gives about four times the strength. 
Inversely, to produce a given ultimate resistance to bend- 
ing, the aluminum beam has about half the weight, thoiigh 
it is not quite so stiff; and to produce a given elastic resist- 
ance, the aluminum beam has less than four-tenths the 
weight, but is only half as stiff'. 
The above comparisons for simple resistance, and for re- 
sistance to bending and stiffness, all so heavily in favor of 
.aluminum, are not complete, however, for passing upon the 
two metals from the standpoint of strength; for the forces 
implied are statical, or else are applied gradually, while in 
the actual service of usual structures, particularly marine 
sti ucttrres, the forces are dynamic, and are applied with full 
efl'ect from the start. The comparison, to be complete, must 
therefore extend to resistance to dynamic forces. 
C— COMPARISON FOE RESISTANCE TO DTNAMIC FORCES. 
Movement, wherever found, represents energy, and is the 
result of work done; and its destruction requires antagon- 
izing energy, antagonizing work. A force, however great, 
FIGt. 16. Work Doue Beyond Elastic Limit, 
Data for Cuives, 
Fijjs. ]5 and 16. 
Modulus of f lastieity, 
Elasticlimit,, 
Elongation within elasticlimit, 
Ultimate tensile s'rength. 
Mild Hteel. 
30.000,fi00 
30,(]00]bs. 
60,0C01bs. 
,S2 
Alum. 
10.000,000 
iS.OOOlbs. 
, of 15 
(deduced 
from 
modulus 
of elast.j 
Work done within the elastic limit, W = ' - X S^, 
done. 
1 
40,0001 bs. 
the ratio of work 
S00C02 
S = lbs. ver sq. in. at elastic limit, i 
E = Modulus of elasticity, T 
V = Volume of body, j 
is thu?. 
10300(00 
times the area of cross section, has 0.46 the weight and 0.82 
the stiffness. ^, ■ - V 
12 For I beams of the same depth, givmg the same elastic 
resistance to bending, the aluminum beam has 1.11 times 
the area of cross section, 0.37 the weight and 0.38 the .stiff- 
HGSS 
13 For angle bars of the same depth, giving the same 
ultimate resistance to bending, the aluminum angle has 1.74 
times the area of cross section, 0.58 the weight and 0.58 the 
stiffness. j ^, • ■ 
14 For angle bars of the same depth, giving the same 
elastic resistance to bending, the aluminum angle has 1.19 
times the area of cross section, 0.39 the weight and 0.38 the 
Of the above results, whose applications to marine con- 
struction are pointed out below, the most striking and most 
significant are those indicating the possibilities of strength 
with limited weight. . .. . 
Thus, for equal weight, m the case of square sections not 
designed primarily for bending, whose simple resistance as 
seen is about twice as great for aluminum for the ultimate 
limit and nearly three times as great for the elastic limit, 
the resistance to bending is nearly three times as great at 
the ultimate limit and four and a half times as great 'it the 
elastic limit, with three times the stiffness. 
unaccompanied by movement, generating no energy, doing 
no work, could extinguish no energy of movement. To ex- 
tinguish energy, the antagonizing force must retreat, and 
the amount of energy extinguished results not only from the 
magnitude of the force, but also from the distance of its 
retreat. If the resisting force varies in magnitude, the 
antagonizing work done is the integral of the products of 
the successive forces by the elementary distances, or is equal 
to the product of the mean force by the distance. 
For comparing the resistance to dynamic forces of steel 
and aluminum, it is thus necessary to determine or compare 
the mean force or resistance that each offers, and the distance 
through which the resistance acts. Taking for the purpose 
of the comparison the case of tension, the force within the 
elastic limit starting at zero, is proportional to the exten- 
sion, so that the mean force up to the elastic limit is equal 
to half the force at the limit. This gives for steel a mean 
force of 15,0001bs. per square inch, and for aluminum a mean 
force of 14,0001bs. per square inch. The elastic exten.sion for 
mild steel being taken at one-eighth of one per cent., the 
work done within the elastic limit is 15000 x 0.00125=18.7 foot 
pounds per square inch of cross section for each foot of 
length. 
Data is lacking on the direct measurement of the elastic ex- 
tension of aluminum, but according to Hlitte, referred to 
above, the modulus of elasticity of aluminum is 10,000,000. 
The modulus for mild steel being taken at 30,000,000, the 
same force would produce three times more elongation in 
aluminum. If the elastic limit reached 30,0001bs. per square 
inch, the elongation would be three-eighths of one per cent. 
Reaching only 28,0001bs per square inch, the actual elonga- 
tion would be ^'^ao X = '20 of one per cent. The work done, 
therefore, within the elastic limit is 14000 x 0.00.35 = 49 foot 
pounds per square inch of cross section for each foot of 
length. The work done within the elastic limit per unit 
area of cross section is therefore 2 61 times greater in alumi- 
num than in steel, as illustrated in Fig. 15. With the same 
weight, the work done by the aluminum piece, which would 
have three times the area of cross section, would be 7 83 times 
as great. 
When it is recalled that structures, particularly marine 
structures, are subject to repeated dynamic forces, which on 
account of their repetition must be extinguished within the 
elastic limit, since they would entail destruction if this limit 
were passed* when it is recalled, thus, that the bulk of usual 
structural resistance is resistance to dynamic forces within 
the elastic limit, the above remarkable result takes oh the 
aspect of a most serious advantage, an advantage for alumi^ 
num that is overwhelming where the structure is not liable 
to be subjected to an unusual or extraordinary force. When, 
however, a single, unusual force is liable to be brought to 
bear, as frequently the case in marine, structures, causing the 
resisting material to pass its elastic limit, the aspect changes 
completely, for at the elastic limit the possible work of alu- 
minum is nearing its limit while the work of steel has 
scarcely begun. Aluminum gives but 10 ^er cent, elongation 
in 2in. , and practically no elongation outside of the 2in. con- 
taining the fracture, while mild steel gives readily 25 per 
cent, elongation in 8in., and the elongation extends to parts 
far removed from the point of fracture. Thus when the 
elastic limit is passed, the bulk of the aluminum piece ceases 
to lend adequate additional assistance, throwing same upon 
the narrow region of ultimate fracture, while with steel the 
whole bulk of the piece continues to contribute proportion- 
ately to the end. 
It is almost as though the whole volume worked with 
steel, while only a section worked with aluminum, and the 
ratio of the two is roughly proportional to tlie length. For 
pieces of even moderate length the difference in work done is 
enormous, as illustrated in Fig. 16. Thus against a single, 
isolated, abnormal, destructive dynamic force, steel gives an 
overwhelmingly larger guarantee, but for usual dynamic 
forces, liable to be indefinitely repeated, aluminum offers 
enormous advantages. 
The application of the results of the above comparisons of 
advantage and disadvantage from the standpoint of strength 
and weight a,re treated below, but these alone are not final 
in determining the choice between two metals: another im- 
portant factor enters, namely, cost. 
ITacht Racing' Association Rules. 
New York, Oct. 26.— Editor Forest and Stream: The pub- 
lication in your issue of Oct. 9 of the racing rules of the pro- 
posed Yacht Racing Association suggests certain points in 
connection with right of way. 
Rule 1 reads as follows: "In maneuvering for a start, up 
to the time of the starting signal, where two or more yachts 
with the wind on the same side are standing toward the line, 
and the weather yacht has the wind fi-eer than the yacht to 
leeward, the leeward yacht shall have the right to hold her 
course." 
This rule is open to the same objections that were the rules 
of similar import heretofore adopted or proposed, in that the 
same dangerous conditions of crowding exist a few seconds 
prior to the starting gun as are found after the gun has been 
given. The words "up to the time of the starting signal" do 
not serve to eliminate the danger which this rule will create. 
This rule gives the yacht the right to hold her course when 
there may be ten or fifty yachts, each manetivering in their 
own way for the one point of advantage on the starting line 
which all alike are seeking. The rule applies only to maneu- 
vering for the start, which means that all are constantly 
shifting helm and that none are actually sailing a 
course. It is an inconsistency to grant rights on a 
course when none are sailing a course, but merely "maneu- 
vering." It practically gives a yacht the right to lay a 
course through a fieet of manetivering yachts, and if she 
chose, to cut them down, for the reason that in all good 
starts there may be a dozen yachts close to the line, and it 
is only possible to avoid collision by the leeward boats keep- 
ing off. A number of boats close together, under these cir- 
cumstances, cannot get themselves clear if a leeward yacht 
insists upon holding her luff. The leeward yacht may swing 
around in a few seconds and be at once in a position to claim 
her rights on a new course, without notice and without being 
seen by the windward boats. In maneuvering for the start 
helmsmen will take chances, and no rule will stop them, and 
if at the last moment a man finds himself in an inextricable 
position, the rule should be so framed as to lessen the 
chances for collision, while the effect of the rule under dis- 
cussion is to increase danger. The old rixle allows every one 
to take all the chances they please, and at the last moment 
all danger is avoided because the leeward boat, which is the 
only one that can do so, must give way. In any case, what 
reason is there for changing the old rule that has always 
worked satisfactorily? The worst thing about this rule is 
that it is unnecessary and contrary to precedent. This 
maneuvering is also against the spirit of the one-gun start. 
The idea is to bring all starters to the line at the same in- 
stant, with an equal chance, and not to force any boat to 
windward of the line, which means in close racing that she 
is out of it from the start. 
Rule 6 reads as follows: "An overtaking yacht shall, in 
every case, as loT>g as an overlap exists, keep clear of the 
yacht which is being overtaken, except as specified in Sec. 
13." In the interest of a clearer definition, and to facilitate 
tile sifting of conflicting evidence in cases of protest, the ad- 
dition of the following words is suggested: "The overtaking 
vessel, if to leeward, must not luff until she has drawn clear 
ahead of the yacht she has overtaken." The leeward yacht 
is protected by the bearing away rule, but should she luff it 
is wholly at her own risk — .she must keep clear. This addi- 
tion to the rule also makes mutual rights more definite when 
two boats are see-sawing for a long time. 
Rule 9 reads as follows: "A yacht may luff as she pleases 
in order to prevent another from passing her to windward, 
provided she begins to luff' before ah overlap is established." 
It is suggested to strike out the words "provided she begins 
to luff before an overlap is established." The justice of this 
is, that if a yacht has secured a lead the rules should aid her 
to retain it; further, under the present rule conflicting evi-. 
dence in cases of foul always exists, for the leading yacht, 
need only luff a hair's breadth to be able to say she luffed^ 
before an overlap was established. If a yacht may luff' as 
she pleases irrespective of the overlap question, then th©t 
overtaking yacht knows definitely what he has to do, which, 
is to keep clear. 
Rule 14 reads as follows: "When a yacht is approaching a 
shore, shoal, rock, vessel or other dangerous obstruction,, 
and cannot go clear by altering her course without fouling 
another yacht, then the latter shall on being hailed by the 
former at once give room; and in case one yacht is forced to 
tack or bear away in order to give room, the other shall also 
tack or bear away, as the case may be, at as nearly the same 
time as is possible without danger of fouling; but should, 
such obstruction be a designated mark in the course, a yacht, 
shall not force another to tack under the provision 3- ofi this . 
rule." 
There seems an Important omission in this rule, which 
would be supplied by adding the following words after the 
words "at once give room"; "provided always an overlap 
has been established before an obstruction is actually 
reached"; otherwise an overtaking yacht is at liberty to 
force a passage between a leading yacht and a shore, for in- 
stance, which is not right. 
E,ule 1 of Marks says that a mark "does not involve any 
question of sea room," which I interpret to mean that one 
yacht cannot call upon another yacht to tack to enable her to 
pass upon a required side of a mark; 
Rule 14 says: "but should such obstruction be a desig- 
nated mark in the course, a yacht shall not force another to, 
tack under the provisions of this rule." The latter provi- 
sion should be discarded, because the two provisions read 
together may be inconsistent; in any case, in face of an ac- 
tual obstruction the rule should not force a vessel into dan- 
ger. Ralph N. Ellis, 
