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What is the most likely length for the cubit of Noah's Ark?The cubit is normally defined as the length from elbow to fingertip, but how long was the arm? (See also Cubit References)

ContentsCubits used in previous studiesSome cubit definitionsCubit IssuesA modern cubitImplications of a long cubit for the Ark

Summary

This study explores common cubit definitions, highlighting the possibility of the ark being larger than current estimates. Previous studies have used a short cubit toshow that there was ample room on the ark. Likewise, stability and seakeeping are also underestimated when calculated using a short cubit. However, a conservativeanalysis of the strength and construction of the ark is exactly the opposite - the long cubit becomes the "worst case" scenario. If the timber hull of Noah's Ark had tosurvive heavy seas, then structural issues (such as leakage due to hull flexing) need to be assessed. If Moses' record of the ark dimensions could possibly imply theuse of the long cubit, then structural analysis should employ this scale as a conservative estimate.

Cubits Used in Previous Studies."Most writers believe the Biblical cubit to be 18 inches (457mm)" (Ref 1, p181). Some studies even use the shortest possible cubit - the 17.5" (445mm) short Hebrewcubit. This is a very conservative estimate in terms of the size of the ark. The following table shows cubit lengths chosen by various authors. This table gives the impression that the 18 inch cubit is the limit to the cubit length, but thereasoning is often nothing more than an attempt to be conservative. These short cubits do not have any strong historical links to early civilization - which were Noah'simmediate descendents.

Year Reference Inch mm Based on...

1961 The Genesis Flood. John C Whitcomb,Henry M Morris, R & R Publishing 1961 17.5" 445

"While it is certainly possible that the cubitreferred to in Genesis 6 was longer than 17.5inches, we shall take this shorter cubit as the

basis for our calculations" p10

1963The Gilgamesh Epic and Old TestamentParallels. A Heidel. Univ of ChicagoPress 1963

18" 457Gives ark dimensions as 450ft long, 75 feet wideand 45 feet high which implies an 18 inch cubit.Heidel claims Babylonian flood account primacy.

1971 The Ark of Noah. Henry M Morris, CRSQVol 8, No 2, p142-144. 1971 18" 457 "Assuming the cubit to be 1.5ft, which is the most

likely value" p142

1975A Comparison of the Ark with ModernShips; Ralph Giannone, CRSQ Vol 12,No1, p53, June 1975

18" 457 "The cubit is understood to be 18 inches, whichseems to be at least approximately correct,..."

1976 The Genesis Record: Henry M Morris,Baker Book House, 1976: p181 17.5" 445

"To be very conservative, assume the cubit tohave been only 17.5 inches, the shortest of allcubits, so far as is known."

1977 Was Noah's Ark Stable? D H Collins,CRSQ Vol 14, No 2, Sept 1977 18" 457

From cubit list in Ramm, Bernard 1956, TheChristian View of Science and Scripture. p229.

Collins says.. "For present purposes I willassume the cubit equal to 18 inches"

1994Safety Investigation of Noah's Ark in aSeaway; S.W.Hong et al , CEN TJ8(1)1994 (AiG)

(17.5") 17.72"

(445)450

"We adopted the common cubit...17.5 inches".After Scott R.B.Y 1959. Weights and Measures of

the Bible. The Archeologist, XXII(2). Actual dimensions used in the study require a

cubit of 450mm, giving the exact figures for 13.5mdepth and 22.5m breadth and 135m length.

1996 Noah's Ark: A Feasibility Study: JohnWoodmorappe, ICR, 1996, p10 18" 457.2

"All the calculations in this work involving the Arkassume a short cubit of 45.72cm." (Wright

G.R.H. 1985 Ancient Building in South Syria andPalestine, Vol 1. E'J.Brill, Leiden. p419)

2001The Most Amazing Ship in the History ofthe World; Prof. Dr. Werner Gitt,Fundamentum; 2001, p7

17.22" 437.5 Siloam tunnel measurement compared to Biblicalrecord (Close to the Hebrew common cubit)

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Some Cubit Definitions

(See also Cubit References)

"The actual length of the cubit varies from 18 inches to 25 inches." (Collins 1977)

Encyclopedia Britannica says the cubit was "usually equal to about 18 inches". In the case of Noah's Ark however, we are interested in the definitions of the earliestcubits - not the most common. "The probability is that the longer was the original cubit." (Easton's Bible dictionary).

Ancient cubits varied in their level of standardization. The Royal Egyptian cubit was remarkably consistent and well defined. In Mesopotamia, cubit standards did notsurvive (probably due to wood construction) - so investigation is limited to clues in building proportions. Not all cubits were defined as the distance from elbow tofingertip either, and there were usually hand-width, finger width (digits) or spans subdividing the cubit. Ancient cubits could be classified into 2 main groups - long and short. The approximate height of the person from whom the cubit was measured is tabulated below.

GROUP CUBIT Inch mm Stature (in) Stature (mm)

Short Cubits

Short Hebrew 17.5" 445 mm 5' 4" 1636 mm Short Egyptian 17.6" 447 mm 5' 5" 1646 mm Common 18" 457 mm 5' 6" 1683 mm

Long Cubits

Babylonian royal 19.8" 503 mm 6' 1" 1852 mm Long Hebrew 20.4" 518 mm 6' 3" 1907 mm Royal Egyptian 20.6" 524 mm 6' 4" 1929 mm

Extra Long Long Babylonian 24" 610 mm 7' 4" 2246 mm

Cubit Issues

Is Noah's cubit too ancient to investigate?.The cubit has disappeared today, although in some countries it was still in use until around 1960 when it was replaced by metric units. There are many examples ofmeasurement systems lasting through the ages. In a continuous civilization, an important base-unit like length is not easily changed. Consider the effort it took todeliberately convert to the metric system. For example, the standard railroad gauge (4ft 8 1/2") is a strange choice - the same gauge that was used in the hand drawncarts of the English coal mines, that found itself in coach-building and eventually trains.. We measure angles using 90 degrees for a right angle. We have never stoppedcounting 7 days as a week. The origin of many measurement systems can go back centuries.

It is worth considering that Noah's cubit would have been the only unit of length immediately after the flood and that Noah's three sons were technically skilled builders.Furthermore, Noah lived for another 350 years in the new world and his son Shem was a contemporary of Abraham. Abraham lived some time in Egypt and hadinfluence (the Pharaoh liked his wife). Noah's cubit could easily appear in these early civilizations. In fact, it is reasonable to expect Noah's cubit to dominate everyculture until the Babel incident. The Hebrew for Cubit is "ammah", derived from mother, as in "mother unit of measure". The same word is used throughout the Old Testament as a unit of length. Thiscould convey the idea of a measurement passed down from an ancestor, who defined the original or 'mother' cubit. Incidentally, the word for mother is commonthroughout many languages.As for standards, the Egyptian cubit has survived intact in cubit standards of wood and stone, as well as in the meticulous dimensions of their architecture. Forthousands of years this cubit varied less than 5%. So it is quite likely that even the actual length of Noah's cubit may have been passed down relatively intact, at leastto a few civilizations.

The Long and the Short of it.Noah's Ark landed in the middle east. The tower of Babel was almost certainly constructed in the same cubit as the ark. If dominant cultures were to travel the leastdistance (or even stay put), then the ancient empires most likely to have continued with Noah's cubit would probably come from Mesopotamia or its vicinity. There arehints that Babylon was built on the site of the original Babel. These cultures would still have an infrastructure that relied on this unit of measure - hence the cubit fromSumeria should be a pretty close estimate. The three ancient civilizations in this area have surprisingly similar cubit definitions - the Egyptian royal cubit more closelydefined then the other units. Since the Hebrews spent 400 years in Egypt, it would be natural to assume Hebrew cubits were an inherited Egyptian measure. However,when the subdivision structure is compared, the Hebrew cubit looks more like a Babylon import.Not that it matters much, look how similar they are;

Civilization Name Inches mm

Mesopotamia (Iraq) kus 20.6" - 20.9" 522-532 Persia (Iran-ish) 20.5" - 21.4" 520-543 Egypt meh 20.6" 524

Known for their meticulous construction and love of mathematics, the Egyptian cubit was an accurate 20.6" (524mm). This length can be quite readily derived from thestudy of construction proportions - such as the chamber measurements in the Pyramids of Gezih. Better than this, actual cubit standards have been well preserved inthe dry conditions. See Petrie's derivations of the royal Egyptian cubit.

In Mesopotamia, wooden "cubit rods" decay in the wet soil, so the length is obtained from buildings that were probably laid out in whole cubits. A copper standard wasunearthed, but the general picture is that cubits outside of Egypt were less exact. Modern scholars find variation in these measurements due in part to the lack ofreliable records, as well as the tolerance limitations of ancient construction.

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Did Moses know two cubits? In his final speech before the Sanhedrin, Stephen described Moses as "educated in all the wisdom of the Egyptians" (Acts 7:22). Moses was obviously familiar with theEgyptian royal cubit and intelligent enough to query its origin. Probably not a Pharaoh - the short length of the typical sarcophagus attests to this. Imagine Moses as ayoung man completing his studies in mathematics being handed the Royal Cubit standard to calculate the area of the palace foyer. Imagine the temptation to put thisfamous cubit against his own arm. Surely Moses would have spotted the anomaly - this was not Pharaoh's forearm.

For this reason, many commentators claim the Egyptian royal cubit was an exaggeration. The problem with this charge is that three different empires all exaggerate -equally. If some Pharaoh had felt the need to appear larger than life, he could at least have chosen a cubit superior to his rivals from the Persian Gulf. Worse still, thelater Egyptian empire was defining a cubit slightly less than the average on the other side of the Arabian desert. A more realistic assumption would be that all theseearly civilizations inherited their cubit length from the one source.

Moses, the author of both Genesis and Deuteronomy applies a different cubit definition when he writes about a contemporary measurement of the enormous bed of KingOg. Not rendered in the NIV, the OKJ translation of Duet 3:11 describes the "cubit of a man" as the unit of measure used here. The giant Og, king of Bashan slept in abed 9 cubits long. By the short cubit (18") this is 13 1/2 feet, by the long cubit almost 16 feet. (Now that IS excessive). In the phrase "cubit of a man", the word forman is "iysh" which is usually associated with a particular man, not "adam" which is more general - like "mankind". Moses, the obvious author/compiler of bothGenesis and Deuteronomy, appears to be making a distinction between the old cubit and the cubit defined by typical forearm length of his day. From Moses' point ofview, Genesis was history, but Deuteronomy was current news "is it not in Rabbath of the children of the Ammon? Deut 3:11". Moses, educated in Egypt and familiarwith the Royal Egyptian cubit of 20.6" (525mm), never made such a distinction in Genesis. This indicates Genesis was measured in an ancient cubit, not by theforearm of Moses' day. Since Moses is demonstrating his awareness of two different cubits, he should have applied himself to the task of defining Noah's cubit also -perhaps with a comment like "according to the cubit of Noah". It appears he was satisfied to let the reader assume it was the "old" measure - not distinguished from theRoyal Egyptian cubit. See also: Revell Bible dictionary

Solomon knew two cubits. 2 Chron 3:3. ...Solomon was instructed for the building of the house of God. The length by cubits after the first measure was threescore cubits...

Since Solomon was capable of piecing a bit of history together, God told him to build with the building cubit (the old long ones), not the everyday commercial cubits (thenew short ones). Later, in Hezekiah's time, the short cubit was used later in Siloam tunnel (confirmed by modern measurements), so the "cubits after the first measure"must have been the other ones. Long.

An exaggerated cubit ... Or are we getting smaller? Shakespeare lived in a tiny house, and the old houses of England had low doors and short beds. The English evolutionistwould naturally assume our increasing stature is a part of the evolution of man. Combine this with a few small EgyptianPharaohs and you have a tidy precept - ancient people were small. Unfortunately, this does not work in Africa wheresupposed 'primitive' tribesmen can average well over 6 feet. It must also ignore the impressive physique of the PacificIslanders 'discovered' by European sailors in the previous century, and a host of other anomalies. Even today,evolutionists are surprised when an ancient human is taller then expected.

The Bible paints a different picture. The original creation was perfect, including extreme longevity and obvious mental andphysical prowess. Good health is more likely to allow a person to grow to their correct height - at least in terms ofpopulation averages. Deteriorating genetics and the startling nutritional ignorance of many ancient urban people (e.gscurvy) would go a long way to explain their short stature.

So if the ante-diluvians were taller, we would expect Noah to be tall. The Ancient cubits correspond to a person around 6ft4" tall. This is tall, but not impossible. In fact it is far more reasonable than an antediluvian cubit of 17.5" (163cm - 5ft 4intall), almost certainly too small for Noah.

Dimensions are not converted. The dimensions of the ark are 300 long, 50 wide and 30 high. These are round numbers and the proportions are excellent for ship stability and sea-keepingperformance. (4) Most readers would assume these were the original numbers God gave to Noah. Assuming these figures were recorded (probably by Shem), Moseswould have compiled them into his manuscript some years later. Being well educated and alert, Moses would have been capable of converting these figures into theequivalent units of his day.

However, the numbers do not appear to have been modified. Conversion from one cubit to another would produce ugly numbers. For example, if the original length hadbeen 261 Royal Babylonian cubits, this would be 251 Royal Egyptian cubits. If Moses had then rounded off to give dimensions in an apparent single significant figure (3hundreds, 5 tens, 3 tens) the error could be as high as 20% (For example; rounding off 251 to the nearest hundred adds an extra 49/251 = 19.5%, which is more thanthe difference between the common short and long cubits.) Worse still, if the depth had been rounded down from 34 to 30 (12%) then the L/D ratio is modified by 35%.The Hong study showed that the dimensions were optimal within 20%. In other words, rounding off to a single significant figure could force the proportions outside theoptimal values.

The most reasonable assumption would be that Moses copied (or was told) the original dimensions as exactly 300 x 50 x 30. Setting the precedent for later Jewishscholars, Moses was no doubt careful to maintain the original numbers.

People like their kings to be tall.The Bible gives many examples of height being revered among men. God is displeased with this tendency, and gives them a dud king that looks the part - King Saul.The fact that he looked like a king indicates that kingship was linked to tall stature.(1 Sam 9:2). Antediluvian superiority aside, Noah's cubit would likely have come froma king, and a king would most likely have been tall.

Reverence for ancestry is another common theme - especially towards the early patriarchs. It would be reasonable to assume that the owner of the forearm definingNoah's cubit was probably someone old and famous. Anyone old was probably taller, and anyone famous was probably tall. Discounting Nephilim due to their extremeungodliness, a 20.6" cubit (6ft 4" person) is then quite a reasonable choice - simply a tall antediluvian.

Some Jewish tradition has Noah is the realm of the giants. The cubit does not show this however, a 20.6" forearm length is a tall person - but no giant. Thismisconception might be explained by the deterioration of health and stature after the flood, making a 20.6" cubit seem superhuman. (e.g. Short stature of EgyptianPharaohs).The Bible gives some examples of height being revered among men. God is displeased with this tendency, and gives them a dud king that looks the part - King Saul.

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The fact that he looked like a king indicates that kingship was linked to tall stature.(1 Sam 9:2). Antediluvian superiority aside, Noah's cubit would likely have come froma king, and a king would most likely have been tall.

The cubit of modern man

Forearm Hand Length. Posterior point of the elbow - dac tylion. (Ref 2)

Procedure: With the beam caliper, measure the horizontal distance from the elbow (olecranon process) to the tip of the middle finger.

Measure your own cubit and compare results. Check if your cubit is around 28% of your height.

The Mishna (Jewish writings) states that the height of a man is 4 cubits (25%)

Forearm functional reach + hand length. Anthropometric data for British military (UK airmen) is freely available (Ref 3). A directcubit was not measured, but can be derived from the functional forearm reach (21) and the hand correction factors (33 & 34), where acubit = 21 + 33 - 34

1987 Measurements for UK aircrew

Measurement 3rdpercentile

50thpercentile

97thpercentile

stature 1658 1783 190121 cubit-grip 390 424 46233 grip correction - ext 178 195 21234 grip correction - clasp 107 117 127 21 + 33 - 34 461 502 547

cubit % of stature 27.80% 28.15% 28.77%

The mid-sized person flying planes in the UK had a cubit of 502mm (19.8"). UK airmen were approx 1.5% taller than the US army measurements of 1988, dropping to a1% advantage in the more competitive 97th percentile. So these servicemen were slightly taller than normal. "Clinical normality" in height is defined as about the range54"-79". The average stature worldwide is 1650mm ́80mm (64.96" ́3.15") for men and 60.5" ́2.95" for women. (Ref 5).

Considering Noah was only 10 generations from Adam and got the bronze medal in the longevity records, it would be safe to assume he was a lot healthier (and taller)than the average male on the planet today, or in the UK air force for that matter. Yet a cubit of only 457mm (18") cubit corresponds to 28% of a mere 1632mm (64.25")stature, well below the world average today. The picture is even more grim and Noah becomes vertically challenged if the 25% Mishna rule is applied. In any case alonger cubit would be a more realistic choice.

The longer measures such as the Nippur cubit or the Royal Egyptian cubit are a better match to archeological evidence, and to the Biblical framework of a creation inbondage to decay. (Romans 8:21). A structural study of Noah's Ark should take the more realistic long cubits into consideration.

Implications of a long cubit for the ark.One reason to prefer the shorter cubit is that it defines a conservatively small ark. This is the best way to defend the ark against accusations of insufficient space -"How could all those animals fit on the ark". Space requirements have been documented by John Woodmorappe in "Noah's Ark: A Feasibility Study". Using the 18"cubit (p50), he concludes that the animals would require only half the floor space - and this is without putting cages one above the other (p16). There is 15 feet betweenfloors which is ample headroom.

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However, when making a case for the structural integrity of the ark, the long cubit should be used. Whenever the forces on an object are mass-related, the stressesincrease in proportion to scale. This defines a maximum size limit to buildings, bridges, aircraft and machines. The larger the vessel, the more critical the structure. Forexample, the bending load applied by waves is considered to be proportional to the length of the vessel to the power of 3.5. See Wave Bending Moment

Stress increases with Size

Consider a rectangular beam (BxD) cantilevered over a length (L), supporting its ownweight (W);

Stress = 3 x W x L / (B x D2).

If you double the scale, you will double all the dimensions, which will increase theweight 8 times.

So Stress = 3 * 8W * 2L / (2B * (2D)2 ) = 6WL/(BD2), which means stress has alsodoubled.

Generally speaking, as scale increases mass related forces (like weight) increase by scale3, but the cross-sectional area only increases by scale2. Since Stress =Force / Area, the stress increases by scale3/scale3, or scale1 - i.e. Stress is proportional to scale. This is known as the square cube law. (Ref 6,7)

Therefore, larger structures need to be more stout. Thus a dinosaur is heavy boned, yet a spider can have whisker thin legs. A flea can leap a hundred times its ownsize, but an elephant can barely get off the ground. A small gymnast has an advantage, a cat can fall out of a tree and walk away, and Tyrannosaurus Rex wasprobably rather clumsy. So the fact that an ant can carry seven times its own weight is not so amazing after all.

In engineering, the same applies to boats, buildings and planes. Have you noticed how we haven't really made things much bigger than we did 30 years ago? We can'tunless we find a material that is many times stronger than what we had before.

Assuming sufficient wave size (probably a reasonable assumption), a longer cubit makes structural strength a more significant issue for the ark.

Large size demands a stout structure.

We need to keep the stress within safe limits, so any increases in size must have a corresponding increase in the stoutnessof structural elements.

In the previous example we wanted to double the length of the beam. This requires a 4 fold increase in breadth and depth,increasing the section modulus 64 times, but the mass only 32 times - thereby maintain the same level of stress.

So building a larger ark is not simply a case of scaling everything up. The increase in length requires a even greater increasein breadth and depth of the structural beams. This obviously results in a maximum size for the vessel - when you end up witha structure of solid wood.

All wood and no rooms!

So how does this effect the ark? The table below shows what happens when you increase the size of the cubit. This assumes a draft of 15 cubits (half the depth)which could be interpreted from the account of the floodwater being more than 15 cubits above the mountain tops. (Indicating that the ark could not run aground) Gen7:20. Though not conclusively fictitious, the Babylonian long cubit of 24" is less likely because it did not appear in multiple empires - the best indication of prior date.(especially prior Babel dispersion).Selecting the most likely cubit is no trivial matter, the mass of the ark could increase at least 50%.

GROUP CUBIT Inch mm Ark Length Tonnes % Increase

Short Cubits

Short Hebrew 17.5" 445 133m 20255 100 %

Short Egyptian 17.6" 447 134m 20604 102 %

Common 18" 457 137m 22041 109 %

Long Cubits

Babylonian royal 19.8" 503 151m 29336 145 %

Long Hebrew 20.4" 518 155m 32085 158 %

Royal Egyptian 20.6" 524 157m 33279 164 %

Extra Long Long Babylonian 24" 610 183m 52245 258 %

Factors that could require increased strength of the hull include hull shape, large wave size, uneven load distribution on the ark, high wind speed, minimal deflection toprevent leakage, collisions with floating debris, launching and beaching loads. One factor that eases structural requirements is the short working life of the ark. Although the occupants may have been confined to the ark for over a year, the voyageitself lasted only 5 months. (or even less if the ark was launched near the end of the 40 days) See also Cubit References

References1. The Genesis Record; Henry M Morris, Baker Books, 19762. National Biodynamics Laboratory http://www.nbdl.org/NCSDB3/Anthropometry/anthro_pages19-29.pdf3. 1988 Anthropometric Survey of U.S. Army Personnel: Methods and Summary Statistics - a technical report (NATICK/TR-89/044) authored by Claire C.Gordon,Thomas Churchill, Charles Clauser, Bruce Bradmiller, John McConville, Ilse Tebbetts, and Robert Walker Wendy Murray

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4. Ministry of Defense.(00-25 Part 2) Human Factors for Designers of Equipment Part 2: Body Size. Feb 1997 http://www.dstan.mod.uk/data/00/025/02000200.pdf5. Anthropometrics and Design. Lecture notes. http://ergo.human.cornell.edu/DEA325notes/anthrodesign.html6. Square cube law (comparative anatomy). http://www.auburn.edu/academic/classes/zy/0301/Topic4/Topic4.html#square.7. Galileo and the Square-cube law. In his book on mechanics Galileo founded the science of strength of materials. He was the first to show that if a structureincreased in all dimensions equally, it would grow weaker. His theoretical basis for this is now known as the square-cube law. The volume increases as the cube oflinear dimensions but the strength only as the square.

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