Introduction

1.1 - What is Volume?

Volume is a numerical quantity. Its use case is to "quantify" the space which could/can be occupied by some object or substance of interest. It's not the same as "space" per se, which is the unoccupied available emptiness that surrounds us and many other objects within this known universe.

Our context denotes that...

Volume is used to quantity spaces from within a larger space.
Volume always inherits at least 3-dimensions.
If a volume inherits from more than 3-dimensions it is denoted a hyper volume.

Hypervolumes whilst they exist are not mainstream science nor are they defined to an accepted international standard thus their context is not covered on volume.cc at present.

1.2 - How is Volume used?

Volume is a numerical quantity we get when we measure something of interest and use well defined formulas which interleave our measurements into "some" scalar output. This scalar (means singular) output is a volume quantity. It's a 3-dimensional cubic unit, it defines a 3-dimensional spacial quantity and it is expressed as a singleton value.

Volume is the output of a measurement using well defined formulas.
Volume is expressed in cubic units such as mm³, cm³, m³... (cm³ is equal to cc).
The context in how we use it as an intelligence is a measurement metric.
The distance between distinct unit types mm³ and cm³ is simply its resolution.
Tape measures and rulers are used to measure linear inputs.
These input scalars are thereafter used to produce an output volume scalar.

1.3 - Why is Volume important?

If we wanted to measure the capacity of a swimming pool, we'd need to solve its volume. Thereafter we'd know how much water it can accommodate.
If we wanted to test the tightness of a coolant tube when its manufactured, we'd need to solve its volume.
Thereafter we can pressure test it and see what volume loss occurs upon its first feed pressurisation and whether it's acceptable (the quality standard).
In construction volume can help us understand what material quantities are necessary to start and finish projects.
They permit us to align with regulatory standards since we can estimate capacity to acceptable degrees of precision.
Shipping and logistics industry rely heavily upon volume measurements since the capacity of containers, vehicles and storage spaces need be known. When known, operators can calculate how many trips are necessary to clear their despatch queue.
Financial and economic industry can use volume to measure market activity.
Volume measurements play an integral part within mathematics and physics. Having the tools and ability of learning to measure and understand volumes helps develop important quantitative and analytical skills.

1.4 - What is Volume.cc?

Live data platform to compute clean accurate volumes.
Global public calculator accessible through a web application.
Solution for simple and more complex volume requirements.
Removes the need for engineers to make and manipulate error prone spreadsheets.
Streamlines the role of quality engineering by replacing cumbersome business processes.
Replaces out dated conventional forms of communication by providing a data protocol.
Provides a peer-2-peer facility to transmit complex parameters.
Allows volumetric datasets to be distributed from OEM manufacturers.
Acts as a public library for future reference and recall.
Offers a protocol which supports traceability, safety and quality.

Solving Volumes

2.1 - Measure a Geometric

Here we have a drinking glass and we'll use it within this example. Now many of us have access to a tumbler and it just so happens that it actually mimics a geometric equal to the cylinder. If we wanted to calculate its volume, we need two input scalars from the object.

These include its diameter and its height. Now given that the walls on this glass are of no interest. We calculate what we term its hollow cylinder. It's the same cylinder but minus the wall width twice. We're left with an inner diameter as opposed to its outer diameter.

Using a well defined formula, we can compute its volume:

... where r is equal to one halving of the inner diameter. Given an inner diameter equal to 6.1 cm (r=3.05) and a height of 13.2 cm. The volume is equal to 385.765587 cm³. Recall from earlier that multiple linear scalar inputs produce a singleton scalar output.

2.2 - Manual Calculation

These volumes can be calculated by hand with or without a calculator albeit its certainly prone to human error. In addition the precision of value PI here indeed will dictate the level of accuracy achieved in its scalar output.

In this instance a PI value with eleven decimal places is required to yield a scalar value which is precise to within seven decimal places. As we've witnessed, it may be an effort to solve a volume for an everyday object and this object is a relatively simple use case.

2.3 - Standardisation

Now our glassing drink in this case should be able to accommodate 385 millilitres (ml = cc) of fluid. This is equal to 38.5% of a litre and exceeds the common capacity of a soda can which is often equal to 330ml. Through this repeatable experiment, we've already witnessed one benefit.

We have a repeatable benchmark to assess whether our drinking glass is suitable for the standard soda can found in most stores. Since we've measured our drinking glass, we could take this tumbler anywhere and rest assured that it will be able to accommodate any soda can with a capacity less than 385 millilitres.

Now lets put it to the test and this experiment can always be used as a fallback to make sure we never break any past repeatable standard. If we were to fill a calibrated measuring jug with 385 millilitres of fluid, it should in theory be able to fill our tumbler with minimal to zero overflow. If it does not then the formula we're using is not well defined. Since we know it is defined, it will only fail if the jug is not calibrated (common problem) or imperfections exist in the circumference.

When we do this and get a good outcome, we can repeat it and it illustrates the concept that repeatability matters because with a repeatable test standard, we have consistency... that is it works and will continue to work.

2.4 - Using Volume.cc

Our web application comes packed with a collection of well defined volumes and features.

It simplifies the complexity of manual calculation and eliminates the most common errors. It has been reviewed and verified by the community to produce reliable outputs and perform the necessary summation and subtraction.

It offers all the ability to:

Load and save datasets locally.
Load and save datasets through our cloud (mobile engineer).
Export datasets on to our live protocol to share globally.
Make complex unconventional volumes for niche use cases.
Define and store repeatable surplus volumes.

2.5 - Automated Calculation

Given a hollow cylinder with a diameter of 6.1 cm and a length of 13.2 cm. We can select the "Cylinder" volume type from the sub menu which appears below the "Volume". Alternatively we may utilise any of the hotkey shortcuts which appear on the right side of this sub menu. In this case, we could hold shift and press the "C" key.

Upon selecting a volume type from the menu, a dialog will appear. Our service allows anyone to solve volumes if they provide scalar inputs with a distinctive label.

After input of a suitable label and accompanied by its scalar inputs, the application will solve the volume for you. The accuracy of the volumes produced is extremely high and a lot more precise than what would alternatively be practical.

2.6 - Substractive Use Case

Here we're going to illustrate a use case when given an imperfect spacial complexity between two objects. We'd need to estimate a 3-dimensional space and the only way to pragmatically achieve this is through estimation.

We can consider the banjo fitting which is often accommodated with a hollow screw in. If we wanted to estimate the spacial complexity range between the inner wall of the banjo and the outer wall of the hollow screw cylinder, we would indeed need to subtract one volume from a higher master volume.

The higher master volume in this case would be the banjo because without the hollow screw in, the spacial complexity would still exist.

Should this screw in insert itself through the banjo's opening, then it should indeed act as a subtractive and the master volume should subtract the attached volume.

Volume.cc facilitates this where we can utilise an ellipsoid to represent our banjo and add a cylinder as the subtractive for the hollow screw in.

Subtractive volumes offer incredible value.

In this instance, our data informs us that the spacial complexity range between the inner banjo wall and the outer wall of the hollow screw in is equal to 130.9 cc (ml). The same technique can be used to estimate the volume of a tyre.

2.7 - How to Subtract

Suppose we need to subtract one object from another. We first add the subtractive object as we would any other regular object.

We next may change its scaling. Setting an objects' scaling = -1 means it is indeed acting as a subtractive. This allows any engineer to subtract one volume from another.

Scaling for each object may be set within the interval [-1, 1]. By default all objects begin with a scale set to 1.

If the overall summation of objects ever dips below 0 due to subtractive volumes, the actual final volume visible in the top right of the calculator will safely default back to zero.

It's not possible on our platform to have negative volumes.

2.8 - Sharing a Dataset

Our platform makes it easy to distribute datasets to other engineers. Given the subtractive example illustrated above, we can quickly dispatch this through the protocol using the export option found within the File menu.

File -> Export -> Publish (Share)

You may add comments to the dataset before the export takes place. These comments will be visible to users accessing the dataset through your URL. Once exported as either a public or private volume, the platform will provide you with an unique URL and ID for the export submission.

Surplus Volumes

3.1 - What is a Surplus

Surplus volumes are repeatable snippets of volumetric data. They are attachable sub volumes onto higher master volumes. If we had a geometric shape which encompasses identical sub components, these repeatable sub components each with their own distinctive measurement would be a surplus volume.

If a component is regular, repeatable and attaches itself into a larger master volume, it is indeed a surplus volume. An example would be repeatable fittings evident on a manufactured part which attaches one section of a part to another (thus establishing a larger part).

In pressure testing industries, these surpluses need to be added so leak rate estimates accurately reflect the parts' inherit quality standard. If they are omitted, the leak rate will not be accurate because the reference volume would be incorrect. We'll cover more upon this shortly.

3.2 - Examination of a Surplus

In a "perfect world" on the supply chain, the fitting seen here would be assigned a specific part number. For our purposes, we will refer to it as a T_PIECE because its shape is akin to a T in the common trade language alphabet.

Now if we were to unscrew its sub fittings and remove its washers, we're left with a sub component which itself encompasses a surplus volume. This surplus volume for our purposes is a data subset we'd need to record for our measurements to have integrity. It's a subset because it's a surplus which belongs to a higher master volume (some larger mechanical part).

Once unbound, we can carefully measure this surplus and comparing it to our available volume list, we'll find that this particular object can be defined using two distinct cylinders.

3.3 - Creating a Surplus

Given a surplus volume upon inspection, we find two cylinders, each has a distinct length albeit both share an equal diameter.

Recall that we use hollow cylinders thus we measure from the internal vertices (inner diameter) and thus disregard any wall properties.

Using two cylinders we can define it using our measurements and find that the spacial complexity for this surplus is equal to 787.3 cubic millimetres.

Once a surplus has been defined, the File->Export sub menu can be used to save it directly onto your account. Surplus volumes are Private by default and are account specific. In order to share them and only if you choose to do so, you need to export them as you would a Network Share and set the share to Public through the "Publish (Share)" option.

3.4 - Accessing Surplus Volumes

Once a surplus volume has been saved to the account. They are available through the "Surplus" menu. Clicking upon a surplus item will introduce it into the volumetric list. Multiple surpluses of the same type are stackable as seen below and are also signified by a x multiplier.

Our service can with ease add supply chain surpluses easily into multiple data sets without having to repeat existing measurement procedures.

3.5 - Benefits of Surplus Volumes

Surplus volumes allow us to define repeatable sub components. They allow us to accurately map the 3-dimensional space occupied by sub component parts. They increase the productivity within an organisation since repeatable surpluses need only be measured and defined once.

Permit supply chain databases to grow organically and correctly categorise fittings.
Increase productivity by removing repeatable processes.
Increase the accuracy of global measurements by utilising mean functions.

If multiple supply chains utilise the same sub parts. Our network can iron out engineer error and use mean metrics to safely soften outliers. By now, we should all know what a surplus volume is, how it can be utilised and what benefits they offer us. Surplus volumes always inherit some hidden volumetric data which if captured allow us to increase our engineering proficiency.

Surplus volumes are critically important. We will study a use case which illustrates how they are fundamental for the success of spacial industries.

Use Case Study

4.1 - Ventilation Pipe

Ventilation pipes can be complex objects in terms of volumetric data sets. They incorporate numerous cylinders and multiple surpluses.

In pressure testing industries, good reference volumes allow products to be tested accordingly to an agreed quality standard. The procedure will have its own specification of what is acceptable and what is not. Its not uncommon for distinct companies to have their own set standards and manufacturers will follow these.

In reality, there exists no perfect seal and the terminology tightness is used to refer to how well fitted a particular part is. Leak testing equipment exists as a step in the firewall chain to prevent poor quality parts reaching global ecosystems. Natural crystallisation processes can and do work to seal minute microscopic leaks which often always go unnoticed in industries which utilise fluid powers.

Leak testing hardware in industry commonly requires a barometer unit (NA often use psi), reference test volume and a max leak rate. Aside from these three additional properties include the time parameters. Adequate amounts of time need be given for parts to be adequately tested. Often, these are the fill, stabilisation and test windows. The leak rate is emitted by a sensor which measures the vibration (a wobble) upon test part pressurisation upon the test window entry.

4.2 - Ventilation Pipe Measurement

Our platform simplifies the entire process of making complex volume datasets. Without volume.cc, a spreadsheet needs to be utilised, maintained and only serves the need of one technician. These spreadsheets may become outdated, corrupt due to version control faults and cannot seamlessly be shared.

This part (described above) in particular has eleven cylinders with multiple surpluses. Most reasonable people would agree the volume requirements become extensive as the complexity of a part increases.

Our service is of great benefit because it can act as a transparent layer between public and private industries. As the complexities within supply chains increase, so does the need for a quality protocol which can manage, store and distribute volumetric datasets.

4.3 - Pressure Decay Rates

The test data available when a bad vent pipe undergoes a repeated pressure test shows really how important a satisfactory reference volume is. The analysis is clear that if the reference volumes are not satisfactory, the manufacturer is simply not testing them to any reasonable standard. Mean (average) leak rates of a part will differ in respect to its reference volume. Higher reference volume means more volume loss per second and ensure the entire space is quantified correctly. This ensures a technique exists to identify problematic gradual leaks and also ensures a more stringent test since the spacial complexity has been adequately accommodated.

Gradual leaks are defined as a test sensor which vibrates (the wobble) upon its first feed pressurisation phrase and then stops wobbling. The part has been pressurised to the correct bar and no wobble thereafter exists because the part is now stable and thereby verified to be leak free. Good parts will inherit a volume loss very close but not equal to zero upon its pressurisation interval.

4.4 - Test Data Analysis

The test data also shows us that when good quality parts are tested, the sensor will vibrate a tiny 2.n cubic millimetres. Its not noticeable but given an extensive amount of data, it indicates that the sensor is one which is indeed actually very well calibrated. Leak detection technologies from leak testing hardware are an excellent piece of engineering.

And because the data trend is repeatable, we get that consistency which makes everyone comfortable with everything because it works and continues to work.

The manufacturer will communicate what volume loss is unacceptable accordingly to their own set of standards. The volume loss (pressure decay) will only be accurate if the reference volume is satisfactory.

Leaks are captured when given satisfactory reference volumes. If reference volumes are not satisfactory, the probability of poor quality parts reaching global ecosystems increases.

This is why quality control is important, a combination of engineering skill followed with a verification technique.

4.5 - Conclusion of Use Case Study

Pressurisation and leak detection technologies are important. They are fundamentally important for the successful execution of spacial industries. Spacial industries encompass any manufacturer using technology to measure spacial domains. And the only difference between the technologies used currently and the challenges out there within space is the scale.

Star ships and multi planetary bases will all inherit distinct geometric shapes, they will all use pressurisation technologies and the pressurisation technology will rely upon sound leak free verification techniques.

Some side notes:

in the context of leak detection hardware, a reference volume is not always equal to the physical volume of an object
we have to consider the test circuitry itself and coil inputs before the actual part is considered
in the case of the ventilation pipe, the manufacturer communicated a tolerated max leak rate of 20 mm³/s
so given that our reference volume was 74100 mm³ with a permitted leak tolerance of 20 mm³
the manufacturer would not accept a deviation greater than: 20 / 74100 = 0.0002%

Putting things into perspective. The quality of the part is exceptional when correctly fitted and often very close (>=0.9998) in terms of the pressurisation quality to the original master sample which would have be verified (signed for) by a prototypes team. This verified part is the sample which all subsequent parts should equal. The master sample mimics the set quality standard and the distance to one signifies its equality to the original sample.

Verification

5.1 - Cylinder and Sphere is a Capsule

On our platform, its possible to combine multiple types to produce a single type. For instance the capsule is useful as it combines both a cylinder with a sphere.

We can test this:

Given a diameter of 5 mm and a length of 250 mm. The sphere is halved and with one half placed on each end of the cylinder resulting in a capsule. The outputs need be uniform as we need repeatability…

5.2 - Sphere and Spherical Cap

One halving of a sphere should equate to a spherical cap which shares the same radius. Given a radius of 20 cm, we reduce the scale of the sphere to 0.5 (one half). Both types evidently emit a spacial complexity of 16755.16 cc.

The spherical cap handles the occasions when the original radius for a sphere was unknown albeit the object of interest results from a cut sphere because their respective shapes are indeed similar to each other.

5.3 - Stadium Frustum

1) if the lower side were to act as a tip akin to the top of a cone with a deep enough resolution and the cone's radius is equal to one halving of the stadium's higher side diameter then the volumes should be equal. In this case, the volume outputs are equal to 261.79 cc.

2) if both sides of a stadium have an equal length and width, it should mimic a perfect cylinder. In this case, the volume outputs are equal to 785.39 cc.

3) the conical frustum (cut cone) can also be used to verify the integrity of the stadium frustum given a matching set of parameters. Outputs 1172.86 cc.

	Public	Academic	Industry
Maximum Objects:	1	10
Surplus Catalogue:		5
Datafile IO:
Cloud Data IO:		5
Netshare (P2P):
Visible Adverts:
Cost:	Nil	Nil	£6.95

Author:	William J.
Publisher:	NLabs Studio
Released:	2024
Industry:	Multiple
Requirements:	Internet access. Modern browser.

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