Slavery

Actually, it can be. Extreme case: 1-tile filler city (the surrounding land being taken by your more advanced ones, or possibly it's in the middile of an arctic wasteland), Kremlin, 8 food from Sushi.

We could just use 5 specialists at all times. If we whip the last one away periodically, we need 8 turns to regrow and gain 45 hammers, an exchange rate of ~5.6:hammers: per specialist-turn sacrificed. Quite good.

If we do a 2-pop whip, we'll grow back in 10 turns missing 13 specialistturns compared to leaving the city alone, giving an exchange rate for ~6.9 per specialistturn.

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If our city is bigger, we want to whip as many specialists away as we can until we reach a certain size - the output of a specialist isn't worth gobbling up 2 food that can be turned into hammers via the whip more efficiently.

At size 10, the food a specialist eats is worth 4.5:hammers:.
At size 15, the food a specialist eats is worth 3.6:hammers:.
At size 20, the food a specialist eats is worth 3:hammers:.

If the city is still healthy that is... which at this time is a non-trivial assumption. Past the health cap, increase the hammer-equivalents by half.

Whipping is sorely underused in the late game, especially in mature cottage economies with corporation support - here we don't have any other useful outlet for surplus food.
 
At size 10, the food a specialist eats is worth 4.5:hammers:.
At size 15, the food a specialist eats is worth 3.6:hammers:.
At size 20, the food a specialist eats is worth 3:hammers:.

Just to be clear these figures are only true with the effect of the Kremlin and they are base hammers. Various multipliers such as forge, factory, OR, HE, MA and drydocks can make quite a lot more hammers depending on what is being whipped. Earlier in the game and when another Civ has built the Kremlin these figures become

At size 5, the food a specialist eats is worth 4:hammers:.
At size 10, the food a specialist eats is worth 3:hammers:.
At size 15, the food a specialist eats is worth 2.4:hammers:.
At size 20, the food a specialist eats is worth 2:hammers:.

These are figures I have commited to memory and at sizes 5,10 and 20 are particularly easy to remember.
 
Does logging a forest before whipping allow you to whip first turn without this penalty?

In short, no.

Longer answer: When you chop the hammers are sort of added into the number of hammers that will be applied at the end of the turn. As such, when you chop on your turn, if you didn't put any hammers towards the item on the previous turn it still won't have any hammers put toward it. Then when you do use the whip, it won't take these hammers into account so not only will you be paying the penalty but also whipping more population (though you can arrange it so this is a good thing).

You'll notice the progress bar for the building has two sepaparate colours too. The lighter grey part is the hammers put towards the project. The darker part is how many will be applied at the end of the turn (and the thing is built at the end of the turn if it fills the bar, NOT at the start of your next turn.
 
@ UncleJJ: Thanks for pointing that out, I hadn't noticed my post was ambiguous as to whether the assumption that we have the Kremlin still applied.

I've valued that wonder highly for a long time, but have only recently come to appreciate the whipping output of deliberately tiny cities (say in a 4-to-2 cycle) throughout the game.
Before corporations, this is achieved by reassigning food resources after my large cities reached their caps (I now tend to build improvements with an eye towards keeping them self-sufficient without the food resources). Naturally, this only works on good land; sometimes even my 'good' cities need all food from resources for something like supporting plains cottages.
 
Whipping is a wonderful process by which angry citizens can be transformed into useful objects. I as a general rule don't whip unless I have happiness/health problems, but I'm no expert at Civ4.
 
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