Wikipedia has a good article on this. There were two common types of crucifixion that the Romans used. The used a simple stake at times. But Jesus was probably crucified on stake with a cross piece on top. It would have looked like an upper case "T:". Also the idea that Jesus would have carried the whole cross as commonly depicted is probably wrong because a cross put up with a body on it would not be very stable. He probably only carried the cross piece and was put up on a stake that was a permanent part of the city just for crucifixions:
en.wikipedia.org
Jesus was a carpenter by trade. This is hard physical work. That meant Jesus was, more than likely, in good athletic condition, due to lifting heavy wood, sawing and hammering for at least a decade. The bible also suggests that Jesus, was unmarried and that he liked to eat out with his friends. The Pharisees called him a drunkard and glutton.
As a carpenter, without children and a wife, Jesus would be middle class, with extra disposable income, and a need to eat out; no wife to cook. If you add this up, Jesus was a young man in good physical shape, who ate well and was not starving and tired. Jesus knew what he would soon face; torture, and he (was) trained to endure this by his lifestyle. His preparation lifestyle also explains how he could wander 40 days in the desert; live off body diet. This stress training would also help him deal with severe dehydration and physical discomfort. He was ready to endure the torture. He would pushed the issue in front of the defensive Pharisees, leading to the inevitable.
I was watching an Easter Special on the ministry of Jesus, leading to his death and resurrection. I had never seen this version of the passion, before. It painted Pontus Pilot as a cruel politician who had advance up the ranks from a soldier. His methods were cruel and forceful. The story showed his soldiers killing dozens of demonstrators at a Passover riot. I often wondered why Pilot is often portrayed as sticking up for Jesus.
The program showed a bible situation where a high ranking Pharisee, Nicodemus questions Jesus in public; to ambush him. He asked Jesus if the Jews should pay taxes, in front of the Roman Guard, to get Jesus. Jesus pauses and then answers Nicodemus; whose face is this on this coin. Nicodemus answers, Caesar! Jesus then says render onto Caesar was is Caesar's and render onto God what is God's. The guard must have told this event to Pilot, which may have made Jesus seem like an ally of Rome, since that answer showed he was not an enemy of Rome. He was only an enemy of the Jews who protested taxes and the Pharisees.Rome ran the crucification and Jesus was killed with distinction by Pilot; cross.
In the psychology of Carl Jung, there are four psychological functions; intellect, emotions, sensations and intuition. These are the four ways all humans orientation themselves to reality. We will think, feel, use five senses and have hunches. These are the same for all humans and would have been the same at the time of Jesus. The 4 point cross, symbolized these four functions for conscious awareness within human nature, with Jesus placed in the center; he was the inner self. The 4 point cross would have archetypically affect; felt unconsciously. This is why it was chosen; timeless human symbolic affect.
The two thieves, one on each side of Jesus, symbolized law. One is capable of looking at reality; four functions. Law requires you learn good and evil, thereby filling your unconscious mind; memory, with both the good and evil data of law. The good person will learn evil but repress it. The two thieves symbolized how law taints even the good person, since it require learning sin, which can become unconscious and compulsive. One thief regrets what he did and can accept his fate; good outside and evil inside. The other thief was evil in and out; denial. Law was also killed in this event. Law was used to kill the son of man.
If you look at the sign of the cross in Christianity, the top is the Father; minds eye, the bottom is the Son; solar plexus, and the two sides; shoulders are the Holy Spirit. Jesus was the son of man; physical or sensory manifestation of God. This feet touch the earth; the son was the sensory function; we could see God in action. The Father is intuition; the creative principle and wisdom. While the Holy spirit is intellect (left side of the cross) and emotions (right side of the cross). The latin for Left is the word sinister. At that time intellect was considered lower, than emotion, but still sanctioned by the spirit.
The vertical post would be only Father and Son, or intuition and sensation, which are opposing functions. This would have led to everlasting conflict between faith; intuition, and seeing is believing; sensory only. The cross; Holy Spirit, adds logic and feeling to help bridge intuition; faith, to sensory need. This gives one reasons and feelings from the spirit of truth to help bridge the opposition implied by just the Father and Son. In innovation, the intuition, when given the drive of emotions, leads to intellectual pursuit, to make it tangible in reality, so others can see; sensory.