to tip something out of upright: to bow it down, lay it down to rest, or make it give way, and of a day, to lean toward evening
One picture sits under every use of this verb: something upright is tipped to an angle. A head drops toward the chest. A face goes down toward the ground. A rank of soldiers buckles and turns back. Greek speakers read the sun's arc the same way, so they could say that the day itself was tilting.
Because the image is physical rather than technical, one Greek verb covers actions that English keeps apart:
- a head bowed at the moment of death, in John 19:30
- faces pushed down toward the ground in fear, in Luke 24:5
- a head put down on something to sleep, in Matthew 8:20
- an enemy line bent back and broken, in Hebrews 11:34
The saying about the Son of Man turns on the plainest of these. Foxes and birds have somewhere to put their heads down at night, and Jesus has nowhere. The same gesture returns at the cross, where John writes that Jesus bowed his head and then gave up his spirit, an order readers have long noticed: the posture of someone finishing a day's work rather than someone being overcome. The ordinary noun built on this verb (κλίνη) names the thing you tip yourself onto, a bed.
The time-of-day use works the same way and is easy to miss in English. When Luke says the day had begun to tilt, or that it had already tilted, he is not giving a clock reading. He is describing the sun sliding down the sky, the hour when travelers start looking for shelter and a host presses a guest to stay.