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best way to accurately cut a rectangle or square from a plywood sheet with underpowered hand tools

I would say the best way is to use power tools. At the bare minimum use a guide - clamp 2 straight boards on either side of the cut with a gap just wide enough for the saw. Aluminum angle works well - it's straight, hard enough that the saw won't wander into it, soft enough not to ruin your saw.

Plywood is a modern product, the grain alternates 90 degrees between layers, and it contains a lot of glue. While handsaws can produce straight cuts (and, in fact, have produced excellent results for centuries) they don't do so well when the material isn't uniform. The wood we had in the days of Louis XIV was old-growth timber carefully chosen for it's best qualities, the wonkier stuff went into the barn or the fireplace.

A circular saw with a guide and/or a couple of clamps (or just some practice) works very well on plywood, and is readily available for under $100.

If you really, really want to continue the old-fashioned way then you need to completely embrace the old fashioned way, and that means not using manufactured materials designed in the age of power tools. Or adopt a hybrid process - I assume you are using plywood because it's a LOT cheaper than large slabs of select, kiln-dried quarter-sawn cabinet-grade red oak, so use the table saw for the straight cuts and the hand tools for everything else. You will spend less on saws this way too, as the glue in the plywood is a bit rough on a plain steel blade - that's why carbide-tipped sawblades are so popular.

best way to accurately cut a rectangle or square from a plywood sheet with underpowered hand tools

I would say the best way is to use power tools. At the bare minimum use a guide - clamp 2 straight boards on either side of the cut with a gap just wide enough for the saw. Aluminum angle works well - it's straight, hard enough that the saw won't wander into it, soft enough not to ruin your saw.

Plywood is a modern product, the grain alternates 90 degrees between layers, and it contains a lot of glue. While handsaws can produce straight cuts (and, in fact, have produced excellent results for centuries) they don't do so well when the material isn't uniform. The wood we had in the days of Louis XIV was old-growth timber carefully chosen for it's best qualities, the wonkier stuff went into the barn or the fireplace.

A circular saw with a guide and/or a couple of clamps (or just some practice) works very well on plywood, and is readily available for under $100.

If you really, really want to continue the old-fashioned way then you need to completely embrace the old fashioned way, and that means not using manufactured materials designed in the age of power tools.

best way to accurately cut a rectangle or square from a plywood sheet with underpowered hand tools

I would say the best way is to use power tools. At the bare minimum use a guide - clamp 2 straight boards on either side of the cut with a gap just wide enough for the saw. Aluminum angle works well - it's straight, hard enough that the saw won't wander into it, soft enough not to ruin your saw.

Plywood is a modern product, the grain alternates 90 degrees between layers, and it contains a lot of glue. While handsaws can produce straight cuts (and, in fact, have produced excellent results for centuries) they don't do so well when the material isn't uniform. The wood we had in the days of Louis XIV was old-growth timber carefully chosen for it's best qualities, the wonkier stuff went into the barn or the fireplace.

A circular saw with a guide and/or a couple of clamps (or just some practice) works very well on plywood, and is readily available for under $100.

If you really, really want to continue the old-fashioned way then you need to completely embrace the old fashioned way, and that means not using manufactured materials designed in the age of power tools. Or adopt a hybrid process - I assume you are using plywood because it's a LOT cheaper than large slabs of select, kiln-dried quarter-sawn cabinet-grade red oak, so use the table saw for the straight cuts and the hand tools for everything else. You will spend less on saws this way too, as the glue in the plywood is a bit rough on a plain steel blade - that's why carbide-tipped sawblades are so popular.

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best way to accurately cut a rectangle or square from a plywood sheet with underpowered hand tools

I would say the best way is to use power tools. At the bare minimum use a guide - clamp 2 straight boards on either side of the cut with a gap just wide enough for the saw. Aluminum angle works well - it's straight, hard enough that the saw won't wander into it, soft enough not to ruin your saw.

Plywood is a modern product, the grain alternates 90 degrees between layers, and it contains a lot of glue. While handsaws can produce straight cuts (and, in fact, have produced excellent results for centuries) they don't do so well when the material isn't uniform. The wood we had in the days of Louis XIV was old-growth timber carefully chosen for it's best qualities, the wonkier stuff went into the barn or the fireplace.

A circular saw with a guide and/or a couple of clamps (or just some practice) works very well on plywood, and is readily available for under $100.

If you really, really want to continue the old-fashioned way then you need to completely embrace the old fashioned way, and that means not using manufactured materials designed in the age of power tools.

best way to accurately cut a rectangle or square from a plywood sheet with underpowered hand tools

I would say the best way is to use power tools. At the bare minimum use a guide - clamp 2 straight boards on either side of the cut with a gap just wide enough for the saw. Aluminum angle works well - it's straight, hard enough that the saw won't wander into it, soft enough not to ruin your saw.

A circular saw with a guide and/or a couple of clamps (or just some practice) works very well on plywood, and is readily available for under $100.

best way to accurately cut a rectangle or square from a plywood sheet with underpowered hand tools

I would say the best way is to use power tools. At the bare minimum use a guide - clamp 2 straight boards on either side of the cut with a gap just wide enough for the saw. Aluminum angle works well - it's straight, hard enough that the saw won't wander into it, soft enough not to ruin your saw.

Plywood is a modern product, the grain alternates 90 degrees between layers, and it contains a lot of glue. While handsaws can produce straight cuts (and, in fact, have produced excellent results for centuries) they don't do so well when the material isn't uniform. The wood we had in the days of Louis XIV was old-growth timber carefully chosen for it's best qualities, the wonkier stuff went into the barn or the fireplace.

A circular saw with a guide and/or a couple of clamps (or just some practice) works very well on plywood, and is readily available for under $100.

If you really, really want to continue the old-fashioned way then you need to completely embrace the old fashioned way, and that means not using manufactured materials designed in the age of power tools.

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best way to accurately cut a rectangle or square from a plywood sheet with underpowered hand tools

I would say the best way is to use power tools. At the bare minimum use a guide - clamp 2 straight boards on either side of the cut with a gap just wide enough for the saw. Aluminum angle works well - it's straight, hard enough that the saw won't wander into it, soft enough not to ruin your saw.

A circular saw with a guide and/or a couple of clamps (or just some practice) works very well on plywood, and is readily available for under $100.