The respective rights and obligations of the two parties to this time charterparty must depend upon its written terms, for there is no special law applicable to the particular form of contract known as a time charterparty.
Per Cockurn CJ in Sandeman v Scurr (1866) L.R. 2 Q.B. 86 at p.96:
The charterer becomes for the time the owner of the vessel; the master and crew become to all intents his servants, and through them the possession of the ship is in him.
Per Mackinnon LJ in Re An Arbitration between Sea and Land Securities Ltd and William Dickinson " Co Ltd (The Alresford),  1 All ER 503 at p.504:
The respective rights and obligations of the two parties to this time charterparty must depend upon its written terms, for there is no special law applicable to the particular form of contract known as a time charterparty. A time charterparty is, in fact, a document which is of a very misleading nature, because the real nature of what is undertaken by the shipowner is disguised by the use of language dating from a century or more ago — language which was then appropriate to a contract of a totally different character. A century ago a time charterparty, then known as a demise charterparty, was an agreement under which the charterer was handed over the possession of the ship of the shipowner to put his servants and crew upon her and to sail her for his own benefit. That form of charterparty, which, as I say, was called a demise charterparty, has long since been obsolete. The modern form of time charterparty party is, in essence, one under which the shipowner agrees with the time charterer that, during a certain named period, the shipowner will render service as a carrier by his servants and crew to carry the goods which are put on board his ship by the time charterer.
In BP Exploration Operating Co Ltd v Chevron Transport (Scotland),  UKHL 50 per Lord Hobhouse of Wood-borough at para 79:
79. A bareboat demise charter differs from the common kinds of charterparty, such as time charters and voyage charters. They involve no transfer of the possession of the vessel to the charterer; they are simply contracts for services to be provided by the ‘owner’ (who may or may not be the actual owner and frequently is just another charterer higher up the line) to the charterer. A voyage charter can be a contract of carriage. A time charter normally includes an express or implied indemnity for the consequences of complying with the charterer’s orders but the vessel remains under the command and control of the owner’s master and crew as if she was being traded for the owner’s own account. A bareboat demise charter by contrast is truly a contract for the hire of the vessel and involves the delivery of the vessel into the possession of the charterer and the control of the vessel resting with the charterer’s employees. The vicarious liability in personam for the delictual or tortious acts of the master and crew rests with their employer, the demise charterer.