In the standards for end caps, the weight of these end caps – a mistake that has persisted for generations!

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According to the head standards, the weight of elliptical heads is generally lower. It stems from the weight issue with the quotes a few days ago. I ran into a weird customer who said that the weight of this end cap, according to the standards I checked, is several kilograms higher than what’s specified. First of all, I want to complain about this client – I give them a quote, and they still expect it to be accurate to within a few hundredths of a kilogram? The weight of the equipment listed in the quote is certainly rounded when determining the price; I usually round it up to 10 kilograms. Secondly, because it’s too much of a hassle to look up the standards, the weight of the end caps has always been calculated using an Excel spreadsheet that I created myself. Compared with the standard, it is a few hundredths of a percent heavier than the weight specified in the standard. I had never thought about it carefully before. So I studied it carefully today. Previously, this formula was actually used to calculate the weight by multiplying the surface area derived from the diameter of the elliptical head by the thickness. This area was calculated using an approximate formula; could it be too large? Since the approximate formula gives a result that’s quite close, I thought maybe it’s calculated using the inner diameter? Calculated using the approximate formula based on the inner diameter – it’s too small! I played around with various calculations; by using the approximate formulas for the inner diameter and mean diameter and then dividing the result by 2, it turned out that the value matched the standard value – what a funny result! Five with random diameters and wall thicknesses were verified. The biggest difference was at 1,000 kilograms, where there was a difference of 0.2 kilograms. Damn it. After conducting further research, I decided to find the exact formula for the area of an ellipse and calculated the area of a standard ellipse using that formula; upon comparison, it turned out to be about 3% higher than the approximate formula! So, the standard weight is 3% lower than the exact weight! Furthermore, the actual weight of the physical object is even greater than what the precise formula calculates! Because elliptical heads are generally cut from circular plates and then formed by stamping or spinning. Molding can change the local thickness, either by thickening or thinning; such areas are actually essentially fixed. However, this does not change the weight. So, the final head weight is the weight of this circular plate. The diameter of this circular plate is the semi-perimeter of the ellipse. At this weight, it is about 6% heavier than the standard! Due to time constraints, only the weight of the elliptical head was compared. It is estimated that other types such as butterfly heads should also have similar problems. The weight wasn’t calculated based on the material dimensions; that’s for sure! The machining allowance for the head edge was not included in the calculation of the aforementioned feeding dimensions