Napoleon's famous for his speed, but what would it be like for someone actually doing the marching? Am I jogging across Europe with a gun in my hand and pack on my back, or does it not feel fast to me at all?
In general, armies became faster in this period by being better organized and marching longer, not by increasing the pace of the march. Speed depends first on how fast subordinates can get their orders, not how fast the conscripts can throw their legs down the roads. Armies usually marched about twelve to eighteen miles in the six-eight hours from dawn to noon, and spent the rest of the day gathering supplies and performing camp chores. However, soldiers usually had a few days rations on their persons and in regimental/battalion/company wagons, as the case may be. As such, they could forego requisitions and extend the length of the daily march into the evening.
However, increased marching rates were sometimes used. The ordinary pace for the French was about 76 steps per minute; their accelerated pace was about 100 steps a minute, and the 'charging pace' was about 140 running steps per minute, cadenced. After the destruction of the Austrian army at Ulm in 1805, the French aggressively exploited the victory, racing down the Danube; the French columns had the appearance of an army routed, but routed forward, baying at the enemy's heels. While marching columns tended to resemble mob scenes, the French had a remarkable ability to quickly form up in perfect order at the sound of the alarm. However, these marches were not necessarily fast. During the devastating operational pursuit after the Battle of Jena, the average speed of the French columns was about 20 km a day. Men who fell behind during marches would be gathered into impromptu depots and formed into provisional units; the army habitually had one halt day a week to give them time to catch up.
Another time-saving measure common during the Napoleonic Wars was the replacement of tents and camps with greatcoats and bivouacs. In the 18th century, armies devoted much labor to carrying and setting up tents for daily halts. These helped preserve the health of the soldier against cold and rain, and furthermore hindered desertion. During the Napoleonic Wars, the growing strength and intrusiveness of the state made manpower cheaper, after a fashion, and armies increasingly dispensed with tents. Instead, soldiers slept in the open around campfires, with coats and bedrolls as their shelter. This was fairly uncomfortable; dew would collect in soldiers' mustaches, and they had to rub their gums in the morning to restore circulation. Over many successive marches, this wore on soldiers more, but freeing up horse transport for artillery or cavalry was considered important enough to risk the increased rates of sickness and desertion. Moreover, armies could break camp faster and start marching sooner without needing to gather and store tents in the morning for the march.
Additionally, the organization of the army's columns could have significant affects on their speed. Even at the same pace, longer columns are slower than shorter ones, as the men at the tail of the column need to march its length in addition to the distance of the march to reach a given point. Moreover, long columns suffer from the 'accordion effect'; minor dislocations at the head of the column reverberate through the rest and accumulate towards the end. In general, more, smaller columns allowed for faster movement at the ordinary pace. Moreover, when circumstances allowed, Napoleon would sometimes push his infantry and cavalry off the roads completely, having them march in masses through the fields while reserving the roads for vehicles and artillery.