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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...
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.
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 spatial quantity and it is expressed as a singleton value.
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 the first lecture that multiple linear scalar inputs produce a singleton scalar output
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.
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
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:
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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. |
Here we're going to illustrate a use case when given an imperfect spatial 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 spatial 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 spatial 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 spatial 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.
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. |
Our platform makes it easy to distribute datasets to other engineers. Given the subtractive example illustrated on our right, we can quickly dispatch this through the protocol using the export option found within the File menu.
File -> Export -> Publish (Share)
There are two ways a dataset can be exported. Public exports appear on our search index and are accessible by the public through the register. If you choose "PRIVATE", the dataset will not appear in the register and will only be visible to recipients who receive from you a unique URL.
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 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. |
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.
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 spatial 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. |
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.
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.
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 spatial industries.
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.
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.
The test data available when a bad vent pipe undergoes a repeated pressure test shows really how important a satisfactory reference volume is. In fact, the evidence is clear that if the reference volume is 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. This is a technique to identify problematic gradual leaks and also ensures a more stringent test.
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.
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 we can recall from lecture 2. Consistency 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.
Leak captured (seen left) when given a satisfactory reference volume. If reference volumes are incorrect, 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. |
Pressurisation and leak detection technologies are important. They are fundamentally important for the successful execution of spatial industries. Spatial industries encompass any manufacturer using technology to measure spatial domains. And the only difference between the technologies used currently and the challenges out there awaiting us 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:
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 manufacturing management. this verified part is the master sample which all subsequent parts must equal. The master sample mimics the quality standard.
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…
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 spatial 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.
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.
Volume.cc is a platform to compute clean accurate volumes. It provides a feature packed calculator to solve both the simple and more complex volume requirements where the quality control needs to be evident.
Volume.cc has essentially removed the need for personnel to use spreadsheets which does not have the facility to natively communicate its data contents. Volume.cc is a solution to solve cumbersome processes which slow existent processes and overcome outdated forms of data communication whilst maintaining data integrity. Its entirely possible now to devise volumetric data sets and share them internally within organisations and/or globally with other engineers around the world within a matter of minutes.
Volume.cc facilitates volume data to be distributed from OEM manufacturers directly to engineers working remotely and permits these complex datasets to be safely stored on our network protocol for future reference and recall. It offers a protocol for its traceability, its safety and overall quality.
Author: | William J. |
Publisher: | NLabs Studio |
Released: | 2024 |
Industry: | Multiple |
Requirements: | Internet access. Modern browser. |