Post by Gordis on Dec 30, 2007 18:27:41 GMT
I decided to try to assess the possible mass of a Palantir.
What facts do we have?
There were two kinds of Palantiri: small and large.
The stones didn’t float in water.
Small stones were about 1 foot in diameter.
Pippin lifted a small stone and carried it.
Big stones cannot be lifted by one man.
Arvedui’s cavalry party carried both a small and a big stone with them all the way to Forochel.
We have no idea about the stone’s density . Maybe the palantir was solid glass (or stone), maybe hollow in the middle. What do we know of Feanorean technology?
But one thing is really helpful:. a palantir didn’t float, so its weight should be MORE than that of a sphere of WATER of the same diameter.
Let us start with a small stone.
I have made some calculations.
The volume of a sphere is (4/3)(pi)(r)^(3).
MASS=(Density)(Volume).
A sphere of WATER 1 foot in diameter weights 14,13 kg. But a small palantir should weight more - or it will float.
Pippin was able to carry it. The hobbit (after his Ent-draught ) has grown somewhat, but still he couldn't have been more than 4 feet tall. According to this convertor: www.onlineconversion.com/length_all.htm
that would be less than 1.22 meter tall. An average 1,2 m child weights around 20-25 kg. The weight of Pippin would be more, as hobbits are heavyset, but still no more than 30-35 kg, I think, as he was not really fat.
He could have hardly lifted more than 15-20 kg, so the Palantir’s density could hardly be much more than that of water, much less than that of glass. Most likely the Palantiri were hollow in the middle.
Thus the possible weight of a small stone ranges from 14,2 to 20 kg.
Now let us take a big stone.
We don’t know its diameter, but first let us take 1m. A sphere of water 1 meter in diameter weights already 523 kg! The stones of Osgiliath and Amon Sul, if they were 1 m in diameter, had to weight even more as the first was lost in the river and the second in the sea. To say "it cannot be lifted by one man" would be an understatement. It cannot be lifted even by five men! I don't see how Arvedui and his retenue could have carried such a big stone with them, horses or no horses.
From the top of my head, I would say that a big stone should weight around 150 kg (that won't be lifted by one man, but it will be by two).
(4/3)(pi)(r)^(3) (1g/cm^(3)) = 150000g
We can calculate: r is about 33 cm. And the diameter would be about 66 cm
So, to fit all the criteria, the Palantiri should be as follows:
Small stone: Diameter 30 cm (one foot) mass = 14,2 -20 kg
Big stone: Diameter 60- 66 cm (about two feet) mass = 114 – 151 kg
Thoughts?
What facts do we have?
There were two kinds of Palantiri: small and large.
The stones didn’t float in water.
Small stones were about 1 foot in diameter.
Pippin lifted a small stone and carried it.
Big stones cannot be lifted by one man.
Arvedui’s cavalry party carried both a small and a big stone with them all the way to Forochel.
We have no idea about the stone’s density . Maybe the palantir was solid glass (or stone), maybe hollow in the middle. What do we know of Feanorean technology?
But one thing is really helpful:. a palantir didn’t float, so its weight should be MORE than that of a sphere of WATER of the same diameter.
Let us start with a small stone.
I have made some calculations.
The volume of a sphere is (4/3)(pi)(r)^(3).
MASS=(Density)(Volume).
A sphere of WATER 1 foot in diameter weights 14,13 kg. But a small palantir should weight more - or it will float.
Pippin was able to carry it. The hobbit (after his Ent-draught ) has grown somewhat, but still he couldn't have been more than 4 feet tall. According to this convertor: www.onlineconversion.com/length_all.htm
that would be less than 1.22 meter tall. An average 1,2 m child weights around 20-25 kg. The weight of Pippin would be more, as hobbits are heavyset, but still no more than 30-35 kg, I think, as he was not really fat.
He could have hardly lifted more than 15-20 kg, so the Palantir’s density could hardly be much more than that of water, much less than that of glass. Most likely the Palantiri were hollow in the middle.Thus the possible weight of a small stone ranges from 14,2 to 20 kg.
Now let us take a big stone.
We don’t know its diameter, but first let us take 1m. A sphere of water 1 meter in diameter weights already 523 kg! The stones of Osgiliath and Amon Sul, if they were 1 m in diameter, had to weight even more as the first was lost in the river and the second in the sea. To say "it cannot be lifted by one man" would be an understatement. It cannot be lifted even by five men! I don't see how Arvedui and his retenue could have carried such a big stone with them, horses or no horses.
From the top of my head, I would say that a big stone should weight around 150 kg (that won't be lifted by one man, but it will be by two).
(4/3)(pi)(r)^(3) (1g/cm^(3)) = 150000g
We can calculate: r is about 33 cm. And the diameter would be about 66 cm
So, to fit all the criteria, the Palantiri should be as follows:
Small stone: Diameter 30 cm (one foot) mass = 14,2 -20 kg
Big stone: Diameter 60- 66 cm (about two feet) mass = 114 – 151 kg
Thoughts?
I'll have to re-read up on what JRRT says about them.
What does everyone think? 
