How many people are needed to eat a korban pesach in one night?

Question

I am trying to figure out mathematically how many people were at a typical Pesach seder in the times of the Temple. I think the number can be approximated from the size, in terms of kosher portions of a typical animal that is suitable for a korban pesach. With that, we could divide by the size of a typical serving of meat. In our times that might be 1/4 pound, but since the korban pesach was to be eaten when satiated, it might be 1/8 pound. So this question boils down to how large is a typical animal that is suitable for a korban pesach. (The weight of kosher portions can be estimated by the weight of dressed meat, which might be found on secular websites related to food.)

Update: Since both a lamb and a kid are valid as a korban peasach, the answer, ideally, would provide information about both. The age of the korban is relevant, since young animals gain weight with time. The korban pesach must be at most one year old (Zevachim pg 25). I do not know the minimum allowable age. So, the question now asks for answers based on species (lamb or kid) the weight at one year and at the minimum acceptable age.

Answer 1

Enlightened by the approaches taken in other answers and encouraged by the large number of views, I suggest this analysis as an answer to my own question.

There is agreement on the web that dressed weight is about 50% (e,g, sites below). There is less agreement on the weight of a lamb of a year of age or under.

This site gives the weight of lambs at 12 months as 20 kg or 44 lbs. http://www.fao.org/wairdocs/ilri/x5522e/x5522e06.htm

This site says the avg weight is 160 lbs at 8 months. https://www.cals.ncsu.edu/an_sci/extension/animal/4hyouth/sheep/sheepfacts.htm

This site gives weights of 33 to 55 kg (73 to 120 lbs) for ages of lamb ranging from 4 to 11 months, with the 33 kg for unweaned 4 months of age. http://www.makingmorefromsheep.com/market-focussed-lamb-and-sheepmeat-production/procedure_3.1.htm

This site says goats gain 1/3 to 1/2 lbs per day and reach 30 to 40 lbs in 66 to 69 days. It says lambs gain .4 to 1 lb per day. http://sheepgoatmarketing.info/education/targetbreeding.php

So 3 of these sites that give lamb weight at a year report: 44, 160, and 120 lbs. The low average seems to be an outlier but I will not throw it out. The average of these 3 estimates is a little over 100 pounds, or dressed weight of 50 lbs. One site said fats and organs are 3% of weight, so I am ignoring them.

Dressed weight includes bone. This site says some 70-75% of a lamb carcass is meat. http://animalscience.psu.edu/extension/meat/pdf/The%20Butcher%20Stole%20My%20Meat.pdf

But raw meat weight is not cooked meat weight. This site says that roasted lamb yields 74%. http://www.ars.usda.gov/SP2UserFiles/Place/80400525/Data/retn/USDA_CookingYields_MeatPoultry.pdf

So, a 100 lb lamb yields 50 pounds of dressed meat, or about 36 lbs of meat to roast, or about 27 pounds after roasting. Assuming a 1/8 pound serving of meat, that comes to 214 people per korban pesach, on average.

A small lamb of 30 lbs would yield a 1/8 lb serving for 64 people.

At lamb at birth weighs about 7 lbs (per one of the above sites). Assuming the above factors apply, that would be 15 people.

What if the participants were really satiated before eating the koran pesach (perhaps due to eating the korban chagiga), and ate only a k'zayis of meat. To find out the impact, we need to estimate the weight of a k'zayis of meat. I tried to do that as follows.

If a k'zayis is a cube 1.2" on edge, or 1.73 cubic inches, and if a cubic foot of water weights 62 lbs, and if meat is mostly water, then one kezayis of meat would weigh 1 oz (if I did the math correctly). If people only ate one k'zayis of meat, the above numbers would have to be multiplied by 2 (since there are 16 oz in a pound or 2 oz in 1/8 lb,)

Perhaps lambs are bigger now than they were in the past. Even so, it seems the seders were large back then.

Answer 2

I am trying to figure out mathematically how many people were at a typical Pesach seder in the times of the Temple.

Not mathematically, but Josephus (Wars book 6 chapter 9 section 3) says:

that feast which is called the Passover, when they slay their sacrifices, from the ninth hour till the eleventh, but so that a company not less than ten belong to every sacrifice… and many of us are twenty in a company

However, it should be noted that Whiston (the translator) had a bias toward this translation. (He notes in a footnote that the number ten-to-twenty matches some Christian belief nicely.) I have not confirmed the accuracy of the translation. (It's apparently from the Ancient Greek "καθ᾽ ἣν θύουσιν μὲν ἀπὸ ἐνάτης ὥρας μέχρις ἑνδεκάτης, ὥσπερ δὲ φατρία περὶ ἑκάστην γίνεται θυσίαν οὐκ ἐλάσσων ἀνδρῶν δέκα, μόνον γὰρ οὐκ ἔξεστιν δαίνυσθαι, πολλοὶ δὲ καὶ συνείκοσιν ἀθροίζονται", but I don't know Ancient Greek.)

Answer 3

Per this PDF, a lean, shorn lamb will provide about 46lb (20.8kg) of meat. Assuming that the weight given excludes the bones and other inedible portions of the animal (such as chelev), if a 1/8lb serving is used, per the OP, we get 368 servings, or that many places at a seder.

Answer 4

What time of the year are lambs born? California is the same zone, temperatures, growing season, etcetera as Israel and can be used to determine Ancient Israel's Lambing and Wheat harvest, for Passover and First Fruits. Yep, and "First Fruits" is about July 4.

Lambs are born during the winter for various reasons. ... Sheep are short day/long night breeders meaning they breed late summer/early fall and consequently their lambs are born in the winter and spring. Second, during the winter, the pasture that sheep normally eat is dormant. – Carroll County Grown carrollgrown.org/why-are-lambs-born-during-the-winter/

Lambs intended for meat are generally sent for slaughter at five to eight months old. The lambs on our farm were born in March, so, depending on the weather and quality of grass over the summer, they may be ready to sell in August. Year on a Sheep Farm | National Sheep Association https://www.nationalsheep.org.uk/know-your-sheep/year-on-a-sheep-farm/

British lambing season. Spring is a significant time in the farming calendar, as farmers get ready to care for more than 15 million ewes preparing to give birth.Feb 15, 2019 British lambing season | Countryside Online https://www.countrysideonline.co.uk/food-and-farming/...the.../british-lambing-season/

California: While lambing will last for six weeks, most of the lambs (and most of the work) will be concentrated between February 23 and March 23 (indeed, 90 percent of our ewes will lamb in this four week period). sacramentovalley.org/stories/remembering-how/

Field Grazing: The average daily gain of lambs on irrigated pasture will vary from 0.2 to .45 pound per lamb per day. Good feeder lambs on desirable irrigated pasture will usually gain at least 0.3 pound per day. ~ California Sheep Production. William C. Weir and Reuben Albaugh

So, the yearling lambs would have been born in February and March to be the Passover lamb, so their weight would be 7 lbs at birth + In Egypt, they WOULDN'T have made or ate ALL or many of the ADDITIONAL dishes in their hurried situation. The point was a quick, long-energizing, nurishment feast before they rushed out of Egypt and walked for many days. Every family was to have a lamb and only add other people, if they weren't going to be able to eat it all. So, I think it is fair to think in Egypt that they ate an average of 1 lb each person from sundown to sunrise, including babies through elderly. So, let's not skimp at a feast by having only one bite sized cube of lamb. Or as the Chic-fil-a cow would say, "Eat mor Chikin".

The Temple will be Rebuilt on Temple Mount.